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24:[["$","$L33",null,{"feature":"flashcards"}],"$L34",["$","$L35",null,{"href":"/gcse/maths/wjec/grade-2-2-6-simplifying-algebra/flashcards","label":"Simplifying Algebra","subjectCode":"gcse_maths__wjec","surface":"flashcards"}],["$","$L36",null,{"runner":["$","div",null,{"className":"min-h-0 flex-1 overflow-hidden bg-background","children":["$","$L37",null,{"decks":[{"id":"bb0c2275-1334-2088-ded7-5f44208b610b","title":"Simplifying Algebra Flashcards","topicId":"cc46fc72-c8f3-4ec0-ee3e-0e82d54322f9","topicSlug":"grade-2-2-6-simplifying-algebra","cards":[{"id":"b88c060c-78f8-6c0f-379b-250ac6f314c8","cardType":"basic","points":1,"front":"In the term $5x$, what is the coefficient?","back":"5","mcqOptions":[{"text":"5","correct":true,"explanation":"The coefficient is the numerical factor multiplying the variable. In $5x$, the number multiplying $x$ is 5, so 5 is the coefficient."},{"text":"$$x$","correct":false,"explanation":"This confuses the variable with the coefficient. The letter $x$ is the variable, while the number multiplying it is 5, making 5 the coefficient."},{"text":"$$5x$","correct":false,"explanation":"This gives the entire algebraic term rather than its coefficient. A coefficient is only the numerical factor, so the coefficient of $5x$ is 5."},{"text":"1","correct":false,"explanation":"A coefficient of 1 is implied when a variable appears alone, as in $x$. Here, $x$ is explicitly multiplied by 5, so the coefficient is 5."}]},{"id":"fc60ec47-5ce5-9389-eac4-dfaee7b53837","cardType":"basic","points":1,"front":"What is a constant in an algebraic expression?","back":"A number on its own with no letter attached (e.g. 4 or -7).","mcqOptions":[{"text":"A number on its own with no letter attached (e.g. 4 or -7).","correct":true,"explanation":"A constant has a fixed numerical value and contains no variable. Therefore, standalone numbers such as 4 and -7 are constants in an algebraic expression."},{"text":"A letter on its own with no number attached (e.g. $x$ or $y$).","correct":false,"explanation":"A letter represents a variable because its value can change. A constant is instead a number with no letter attached, such as 4 or -7."},{"text":"A number multiplying a letter in a term (e.g. 4 in $4x$).","correct":false,"explanation":"A number multiplying a variable is a coefficient, not a constant term. A constant appears on its own with no letter attached, such as 4 or -7."},{"text":"A term containing the same letter and power (e.g. $4x$ or $-7x$).","correct":false,"explanation":"Terms with matching letters and powers are like terms, not constants. A constant is a standalone number with no letter attached, such as 4 or -7."}]},{"id":"dd2f8db9-406e-d48e-e2de-ce0e78dc5c50","cardType":"basic","points":1,"front":"Which part of a term must be identical for two terms to be considered 'like terms'?","back":"The letter part (including the power).","mcqOptions":[{"text":"The letter part (including the power).","correct":true,"explanation":"Like terms must contain exactly the same variables raised to the same powers. Their numerical coefficients may differ, so $3x^2$ and $-5x^2$ are like terms."},{"text":"The coefficient (including the sign).","correct":false,"explanation":"Like terms may have different coefficients and signs; for example, $3x$ and $-7x$ are like terms. Their letter parts, including powers, must be identical."},{"text":"The total value (including the coefficient).","correct":false,"explanation":"Terms do not need equal values to be like terms. They must instead have identical letter parts and powers, as with $2a^3$ and $9a^3$."},{"text":"The number part (including the sign).","correct":false,"explanation":"Matching number parts do not make terms alike; $4x$ and $4y$ are not like terms. The letter part, including every power, must be identical."}]},{"id":"20feba41-0445-5c55-c703-bdd2178b2d37","cardType":"cloze","points":null,"front":"Simplify $r + r + r + r = \\text{[...]}.","back":"Simplify $r + r + r + r = \\boxed{4r}.","mcqOptions":[{"text":"$$4r$","correct":true,"explanation":"The four terms are identical, so their coefficients add: $1+1+1+1=4$. Therefore, four lots of $r$ simplify to $4r$."},{"text":"$$r^4$","correct":false,"explanation":"This confuses repeated addition with repeated multiplication. Adding four identical $r$ terms gives $4r$; $r^4$ would result from multiplying $r$ by itself four times."},{"text":"$$5r$","correct":false,"explanation":"This off-by-one error counts five copies of $r$, but the expression contains only four. Adding their coefficients gives $1+1+1+1=4$, so the result is $4r$."},{"text":"$$4+r$","correct":false,"explanation":"The number of identical terms becomes a coefficient rather than a separate constant. Four copies of $r$ combine as $4r$, not as an addition of 4 and $r$."}]},{"id":"c49560a0-b698-a250-2f3c-e3b122f415c8","cardType":"basic","points":2,"front":"Simplify $6t + 3t - 4t$.","back":"$$5t$","mcqOptions":[{"text":"$$5t$","correct":true,"explanation":"All three terms are like terms, so their coefficients combine: $6+3-4=5$. Keeping the common variable $t$ gives the simplified expression $5t$."},{"text":"$$13t$","correct":false,"explanation":"This treats the negative coefficient as positive and adds all three magnitudes. The coefficients must be calculated as $6+3-4=5$, giving $5t$."},{"text":"$$7t$","correct":false,"explanation":"This likely subtracts 3 instead of 4 or mishandles the signs. Combining the coefficients correctly gives $6+3-4=5$, so the result is $5t$."},{"text":"$$5$","correct":false,"explanation":"This correctly combines the coefficients but drops the variable. Since every term contains $t$, the simplified result must retain that common letter, giving $5t$."}]},{"id":"d694df1e-d24c-74fe-71c5-107327996a8c","cardType":"basic","points":1,"front":"In the expression $9a - 2a$, which term does the minus sign belong to?","back":"The term following it ($-2a$).","mcqOptions":[{"text":"The term following it ($-2a$).","correct":true,"explanation":"A subtraction sign forms part of the coefficient of the term immediately following it. Therefore, the second term is negative and should be treated as $-2a$."},{"text":"The term before it ($9a$).","correct":false,"explanation":"A minus sign applies to the term that follows it, not the term before it. Thus, $9a$ is positive and the following term is $-2a$."},{"text":"Both terms together ($9a-2a$).","correct":false,"explanation":"The minus sign does not make the whole expression negative. It belongs to the following term, giving a positive first term $9a$ and a negative second term $-2a$."},{"text":"The letter only ($-a$).","correct":false,"explanation":"The sign belongs to the entire following term, including its numerical coefficient. The negative term is $-2a$, rather than the minus sign applying only to the letter."}]},{"id":"189c4a3a-6ecd-1566-7aef-b136ace315ce","cardType":"cloze","points":null,"front":"To simplify $8g + 4h - 3g + 2h$:

Collect $g$ terms: $\\text{[...]}$
Collect $h$ terms: $6h$

","back":"To simplify $8g + 4h - 3g + 2h$:

Collect $g$ terms: $\\boxed{5g}$
Collect $h$ terms: $6h$

","mcqOptions":[{"text":"$$5g$","correct":true,"explanation":"The $g$ terms are $8g$ and $-3g$. Subtracting their coefficients gives $8-3=5$, so they combine to make $5g$."},{"text":"$$11g$","correct":false,"explanation":"This ignores the minus sign and adds 3 to 8. The second $g$ term is $-3g$, so the correct calculation is $8-3=5$, giving $5g$."},{"text":"$$5$","correct":false,"explanation":"This combines the coefficients correctly but drops the variable. Because both collected terms contain $g$, the result must also contain $g$, giving $5g$."},{"text":"$$-5g$","correct":false,"explanation":"This reverses the subtraction and calculates $3-8$ rather than $8-3$. Following the original order gives $8g-3g=5g$, which is positive."}]},{"id":"8d13ecb1-bd45-6868-65f0-b34b1b15fed1","cardType":"cloze","points":null,"front":"To simplify $8g + 4h - 3g + 2h$:

Collect $g$ terms: $5g$
Collect $h$ terms: $\\text{[...]}$

","back":"To simplify $8g + 4h - 3g + 2h$:

Collect $g$ terms: $5g$
Collect $h$ terms: $\\boxed{6h}$

","mcqOptions":[{"text":"$$6h$","correct":true,"explanation":"The $h$ terms are $4h$ and $2h$. Adding their coefficients gives $4+2=6$, so the collected $h$ terms simplify to $6h$."},{"text":"$$2h$","correct":false,"explanation":"This subtracts the coefficients even though both $h$ terms are positive. They should be added: $4h+2h=6h$, so the collected result is $6h$."},{"text":"$$8h$","correct":false,"explanation":"This likely multiplies the coefficients instead of adding them. Collecting like terms requires $4+2=6$, so $4h+2h$ simplifies to $6h$."},{"text":"$$6$","correct":false,"explanation":"This adds the coefficients correctly but omits the common variable. Since both terms contain $h$, their sum must retain it, so the result is $6h$."}]},{"id":"71120a14-4115-62a4-5fa1-882b8dfbe280","cardType":"basic","points":3,"front":"Simplify $5a + 6 - 2a + 3$.","back":"$$3a + 9$","mcqOptions":[{"text":"$$3a + 9$","correct":true,"explanation":"The like terms $5a$ and $-2a$ combine to give $3a$, while the constants $6$ and $3$ combine to give $9$."},{"text":"$$7a + 9$","correct":false,"explanation":"This treats $-2a$ as positive and adds the coefficients. Keeping its negative sign gives $5a-2a=3a$, so the correct simplification is $3a+9$."},{"text":"$$3a + 3$","correct":false,"explanation":"This subtracts the constants instead of adding them. Both constants are positive, so $6+3=9$ and the expression simplifies to $3a+9$."},{"text":"$$12a$","correct":false,"explanation":"This incorrectly combines constants with terms containing $a$. Only like terms can be collected, giving $5a-2a=3a$ and $6+3=9$, so the answer is $3a+9$."}]},{"id":"477d3783-9165-0877-8ebb-5bb79d356123","cardType":"basic","points":1,"front":"Why can the expression $3a + 4b$ not be simplified?","back":"They are unlike terms (different letter parts).","mcqOptions":[{"text":"They are unlike terms (different letter parts).","correct":true,"explanation":"Terms can be added or subtracted only when their letter parts match. Since one term contains $a$ and the other contains $b$, they cannot be collected."},{"text":"They have different coefficients (3 and 4).","correct":false,"explanation":"Different coefficients do not prevent simplification; for example, $3a+4a=7a$. The expression cannot be simplified because $a$ and $b$ make the terms unlike."},{"text":"They contain two variables (letters cannot be added).","correct":false,"explanation":"Expressions containing two variables can sometimes be simplified when like terms occur. Here, $3a$ and $4b$ cannot combine specifically because their letter parts are different."},{"text":"They are already factorised (nothing can be combined).","correct":false,"explanation":"The expression is not written as a product, so it is not factorised. It cannot be collected because $3a$ and $4b$ are unlike terms with different letter parts."}]},{"id":"b292cf7b-d9aa-65aa-2d40-2702103300ba","cardType":"cloze","points":null,"front":"In algebra, $a \\times b$ is written as $\\text{[...]}$.","back":"In algebra, $a \\times b$ is written as $\\boxed{ab}$.","mcqOptions":[{"text":"$$ab$","correct":true,"explanation":"In algebra, the multiplication sign between letters is conventionally omitted. Writing the letters next to each other gives $ab$, which means $a$ multiplied by $b$."},{"text":"$$a+b$","correct":false,"explanation":"A plus sign represents addition rather than multiplication. Algebraic multiplication is written by placing the letters together, so $a\\times b$ is written as $ab$."},{"text":"$$a-b$","correct":false,"explanation":"A minus sign represents subtraction, not multiplication. The standard algebraic notation omits the multiplication sign and writes the two factors together as $ab$."},{"text":"$$\\frac{a}{b}$","correct":false,"explanation":"Writing $a$ over $b$ represents division of $a$ by $b$. For multiplication, the letters are placed next to each other, giving $ab$."}]},{"id":"68734c47-eeaa-b379-0b48-7f45a5114228","cardType":"basic","points":1,"front":"Simplify $5 \\times 4x$.","back":"$$20x$","mcqOptions":[{"text":"$$20x$","correct":true,"explanation":"Multiply the numerical factors to get $5\\times4=20$, then retain the variable $x$. Therefore, $5\\times4x$ simplifies to $20x$."},{"text":"$$9x$","correct":false,"explanation":"This comes from adding $5$ and $4$ instead of multiplying them. The operation is multiplication, so $5\\times4=20$ and the correct result is $20x$."},{"text":"$$20$","correct":false,"explanation":"This multiplies the numerical factors correctly but drops the variable. Since $x$ remains a factor, $5\\times4x$ simplifies to $20x$, not just $20$."},{"text":"$$20x^2$","correct":false,"explanation":"This introduces an extra factor of $x$. Only one $x$ appears in the original expression, so its power remains $1$ and the result is $20x$."}]},{"id":"a073e584-bfc1-fbd0-0004-a954b70b574c","cardType":"basic","points":2,"front":"Simplify $3p \\times 6q$.","back":"$$18pq$","mcqOptions":[{"text":"$$18pq$","correct":true,"explanation":"Multiply the coefficients to obtain $3\\times6=18$, then write the variable factors together as $pq$. This gives the simplified product $18pq$."},{"text":"$$9pq$","correct":false,"explanation":"This adds the coefficients $3$ and $6$ instead of multiplying them. Because the operation is multiplication, the coefficient is $18$, giving $18pq$."},{"text":"$$18p+q$","correct":false,"explanation":"The variables are factors, so they must remain multiplied rather than be separated by addition. Multiplying coefficients and writing variables together gives $18pq$."},{"text":"$$18p^2q^2$","correct":false,"explanation":"The variables have been squared even though each appears only once. Multiplying $3p$ by $6q$ gives coefficient $18$ and variable part $pq$, so the result is $18pq$."}]},{"id":"14226307-e327-e8b9-4c70-1e90c712f7d9","cardType":"basic","points":1,"front":"Identify the common mistake when simplifying $2a \\times 5b$.","back":"Adding the coefficients instead of multiplying them (result should be $10ab$, not $7ab$).","mcqOptions":[{"text":"Adding the coefficients instead of multiplying them (result should be $10ab$, not $7ab$).","correct":true,"explanation":"When multiplying algebraic terms, their coefficients must also be multiplied. Since $2\\times5=10$ and $a\\times b=ab$, the correct product is $10ab$, not $7ab$."},{"text":"Subtracting the coefficients instead of multiplying them (result should be $10ab$, not $3ab$).","correct":false,"explanation":"Although subtraction would also be an invalid operation, the stated common error producing $7ab$ comes from adding $2$ and $5$. The coefficients should be multiplied to give $10ab$."},{"text":"Multiplying the coefficients but adding the letters (result should be $10ab$, not $10a+10b$).","correct":false,"explanation":"Adding the letters is an error, but it does not explain the specific incorrect result $7ab$. That result comes from adding the coefficients instead of multiplying them; the answer is $10ab$."},{"text":"Adding the coefficients and the letters separately (result should be $10ab$, not $7a+7b$).","correct":false,"explanation":"This describes a different incorrect method and result. The identified mistake is adding only the coefficients to obtain $7ab$; multiplying $2$ and $5$ correctly gives $10ab$."}]},{"id":"e6e03970-d8f4-be72-9e57-f7752ee3b64d","cardType":"basic","points":1,"front":"What does a power (or index) indicate in algebra?","back":"How many times a letter is multiplied by itself.","mcqOptions":[{"text":"How many times a letter is multiplied by itself.","correct":true,"explanation":"A power records repeated multiplication of the same base. For example, $a^3$ means $a\\times a\\times a$, so there are three factors of $a$."},{"text":"How many times a letter is added to itself.","correct":false,"explanation":"Repeated addition produces a multiple, not a power; for example, $a+a+a=3a$. A power indicates repeated multiplication, so $a^3=a\\times a\\times a$."},{"text":"The number that is multiplied by the letter.","correct":false,"explanation":"The number multiplying a letter is its coefficient, as $3$ is in $3a$. A power instead shows how many times the letter is multiplied by itself."},{"text":"How many different letters are multiplied together.","correct":false,"explanation":"A power counts repeated factors of the same base, not the number of different variables. For example, $a^3$ contains three factors of $a$."}]},{"id":"746d0928-ef41-c1f9-8380-7201eb955a6d","cardType":"cloze","points":null,"front":"Simplify $z \\times z \\times z = \\text{[...]}.","back":"Simplify $z \\times z \\times z = \\boxed{z^3}.","mcqOptions":[{"text":"$$z^3$","correct":true,"explanation":"There are three identical factors of $z$, so index notation uses an exponent of $3$. Thus, $z\\times z\\times z$ simplifies to $z^3$."},{"text":"$$3z$","correct":false,"explanation":"This confuses repeated multiplication with repeated addition. While $z+z+z=3z$, the product of three factors of $z$ is $z^3$."},{"text":"$$z^2$","correct":false,"explanation":"An exponent of $2$ represents only two factors, $z\\times z$. Since the expression contains three factors of $z$, the correct result is $z^3$."},{"text":"$$3z^3$","correct":false,"explanation":"The exponent already records the three factors of $z$, so no coefficient of $3$ is introduced. The product is $z^3$, with an implied coefficient of $1$."}]},{"id":"d746f253-7d4f-44e6-7651-1fa908e28c12","cardType":"basic","points":2,"front":"Contrast the simplified forms of $x + x$ and $x \\times x$.","back":"

$x + x = 2x$
$x \\times x = x^2$

","mcqOptions":[{"text":"

$x + x = 2x$
$x \\times x = x^2$

","correct":true,"explanation":"Adding two identical terms gives a coefficient of 2, while multiplying $x$ by itself gives a power of 2. Addition and multiplication therefore simplify differently."},{"text":"

$x + x = x^2$
$x \\times x = 2x$

","correct":false,"explanation":"This reverses the rules for addition and multiplication. Adding identical terms gives $x + x = 2x$, whereas multiplying identical factors gives $x \\times x = x^2$."},{"text":"

$x + x = 2x$
$x \\times x = 2x$

","correct":false,"explanation":"The addition has been simplified correctly, but multiplication does not add coefficients. Since $x$ is multiplied by itself, $x \\times x = x^2$, not $2x$."},{"text":"

$x + x = x^2$
$x \\times x = x^2$

","correct":false,"explanation":"The multiplication has been simplified correctly, but powers are not created when terms are added. Collecting two $x$ terms gives $x + x = 2x$, not $x^2$."}]},{"id":"7721fd78-6e30-2281-4106-4c373ce2a049","cardType":"basic","points":1,"front":"Are $x^2$ and $x$ like terms?","back":"No (they have different powers).","mcqOptions":[{"text":"No (they have different powers).","correct":true,"explanation":"Like terms must contain exactly the same variables raised to the same powers. Since $x^2$ has power 2 and $x$ has power 1, they are not like terms."},{"text":"Yes (they have the same variable).","correct":false,"explanation":"Sharing the variable $x$ is not sufficient for terms to be like terms. Their powers must also match, so $x^2$ and $x$ are not like terms."},{"text":"Yes (they have consecutive powers).","correct":false,"explanation":"Powers being consecutive does not make terms alike. Like terms require identical variable parts, so the different powers in $x^2$ and $x$ mean they cannot be collected."},{"text":"No (they have different coefficients).","correct":false,"explanation":"Coefficients may differ without preventing terms from being like terms. The real reason is that $x^2$ and $x$ have different powers, so their variable parts do not match."}]},{"id":"5b9d6bb0-9734-64b6-4916-030129361aae","cardType":"cloze","points":null,"front":"Simplify $4x^2 - 3x + 2x^2 + 5x$:

Collect squared terms: $\\text{[...]}$
Collect $x$ terms: $2x$

","back":"Simplify $4x^2 - 3x + 2x^2 + 5x$:

Collect squared terms: $\\boxed{6x^2}$
Collect $x$ terms: $2x$

","mcqOptions":[{"text":"$$6x^2$","correct":true,"explanation":"The squared terms are like terms, so their coefficients can be added: $4x^2 + 2x^2 = (4 + 2)x^2 = 6x^2$."},{"text":"$$6x^4$","correct":false,"explanation":"Adding like terms does not add their powers. The coefficients 4 and 2 are added while the power remains 2, giving $4x^2 + 2x^2 = 6x^2$."},{"text":"$$8x^2$","correct":false,"explanation":"This comes from multiplying the coefficients rather than adding them. Because the expression contains addition, $4x^2 + 2x^2$ has coefficient $4 + 2 = 6$, giving $6x^2$."},{"text":"$$2x^2$","correct":false,"explanation":"This subtracts the coefficients instead of adding them. Both squared terms are positive, so $4x^2 + 2x^2 = (4 + 2)x^2 = 6x^2$."}]},{"id":"8e886b58-54c2-d9f2-88eb-051fd4f7f4da","cardType":"cloze","points":null,"front":"Simplify $4x^2 - 3x + 2x^2 + 5x$:

Collect squared terms: $6x^2$
Collect $x$ terms: $\\text{[...]}$

","back":"Simplify $4x^2 - 3x + 2x^2 + 5x$:

Collect squared terms: $6x^2$
Collect $x$ terms: $\\boxed{2x}$

","mcqOptions":[{"text":"$$2x$","correct":true,"explanation":"The linear terms are like terms, so combine their coefficients: $-3x + 5x = (-3 + 5)x = 2x$."},{"text":"$$8x$","correct":false,"explanation":"This ignores the negative sign on $-3x$ and adds 3 and 5. The signed coefficients must be combined as $-3 + 5 = 2$, giving $2x$."},{"text":"$$-2x$","correct":false,"explanation":"This reverses the subtraction and gives the wrong sign. Starting at $-3$ and adding 5 gives 2, so $-3x + 5x = 2x$."},{"text":"$$-8x$","correct":false,"explanation":"This treats both coefficients as negative. Only the coefficient of $3x$ is negative, so the correct calculation is $-3 + 5 = 2$, producing $2x$."}]},{"id":"4e37aeb2-6adb-5ce0-98e4-077559de3897","cardType":"basic","points":1,"front":"Simplify $\\frac{15k}{5}$.","back":"$$3k$","mcqOptions":[{"text":"$$3k$","correct":true,"explanation":"Dividing the coefficient 15 by 5 gives 3, while the variable $k$ remains unchanged. Therefore, $\\frac{15k}{5} = 3k$."},{"text":"$$10k$","correct":false,"explanation":"This subtracts 5 from 15 instead of dividing by 5. The denominator requires division, so $15 \\div 5 = 3$ and the simplified expression is $3k$."},{"text":"$$75k$","correct":false,"explanation":"This multiplies 15 by 5 rather than dividing by the denominator. The coefficient should be calculated as $15 \\div 5 = 3$, giving $3k$."},{"text":"$$3k^2$","correct":false,"explanation":"Dividing numerical coefficients does not increase the power of the variable. Since only one factor of $k$ is present, $\\frac{15k}{5}$ simplifies to $3k$."}]},{"id":"7332c40d-d967-3f4b-e1ef-8c513f024743","cardType":"basic","points":1,"front":"Simplify $\\frac{6d}{d}$.","back":"6","mcqOptions":[{"text":"6","correct":true,"explanation":"For $d \\ne 0$, the factor $d$ appears in both numerator and denominator and cancels because $\\frac{d}{d} = 1$. This leaves 6."},{"text":"$$6d$","correct":false,"explanation":"This leaves the common factor $d$ uncancelled. For $d \\ne 0$, $\\frac{d}{d} = 1$, so $\\frac{6d}{d} = 6$."},{"text":"1","correct":false,"explanation":"Cancelling $d$ does not also cancel the coefficient 6. Since $\\frac{d}{d} = 1$, the expression becomes $6 \\times 1 = 6$."},{"text":"$$6d^2$","correct":false,"explanation":"Division by $d$ reduces the number of factors of $d$ rather than increasing its power. The numerator’s $d$ cancels with the denominator’s $d$, leaving 6."}]},{"id":"0b78b42b-ec04-0ea2-e737-c6238ec095e8","cardType":"basic","points":2,"front":"Outline the two steps to simplify $\\frac{8m + 4m}{4}$.","back":"

Collect like terms on the numerator ($12m$)
Divide the result by 4 ($3m$)

","mcqOptions":[{"text":"

Collect like terms on the numerator ($12m$)
Divide the result by 4 ($3m$)

","correct":true,"explanation":"The numerator contains like terms, so $8m + 4m = 12m$. Dividing the combined numerator by 4 then gives $\\frac{12m}{4} = 3m$."},{"text":"

Collect like terms on the numerator ($12m$)
Multiply the result by 4 ($48m$)

","correct":false,"explanation":"The numerator is combined correctly, but a denominator of 4 means divide rather than multiply. After obtaining $12m$, calculate $12m \\div 4 = 3m$."},{"text":"

Multiply the terms on the numerator ($32m^2$)
Divide the result by 4 ($8m^2$)

","correct":false,"explanation":"The numerator contains addition, so its like terms must be added rather than multiplied. This gives $8m + 4m = 12m$, followed by $12m \\div 4 = 3m$."},{"text":"

Collect like terms on the numerator ($12m$)
Subtract 4 from the result ($8m$)

","correct":false,"explanation":"The first step is correct, but the fraction bar represents division, not subtraction. The combined numerator $12m$ must be divided by 4, giving $3m$."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Unit 1"},"heading":"Simplifying Algebra","title":"Simplifying Algebra Flashcards","topbar":{"backHref":"/gcse/maths/wjec/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"cc46fc72-c8f3-4ec0-ee3e-0e82d54322f9","walled":"$L39"}],"$L3a","$L3b"]