What is the most common mistake when expanding brackets?

The most common mistake is multiplying only the first term inside the bracket. In $a(b+c)$, the multiplier $a$ must multiply both $b$ and $c$, giving $ab+ac$.

How do I expand brackets with a negative number outside?

Multiply the negative number by every term inside the bracket and check each sign separately. For example, $-2(x-4)=-2x+8$ because a negative multiplied by a negative is positive.

How many products should double brackets create?

Two binomials initially create four products. In $(a+b)(c+d)$, calculate $ac$, $ad$, $bc$ and $bd$, then collect any like terms.

Can I check an expansion by substitution?

Yes. Substitute the same convenient value into the original and expanded expressions. Different results prove that an error has occurred, although matching results for one value alone are not a complete algebraic proof.

Should I collect like terms while expanding brackets?

It is safer to expand every bracket first and collect like terms afterwards. Keeping the stages separate reduces missed products and makes negative-sign errors easier to find.

Common Expanding Brackets Mistakes in GCSE Maths

A bracket can look harmless. Then one missed multiplication or negative sign changes the whole expression.

The common mistakes with expanding brackets in GCSE Maths usually come from rushing one of three things: multiplying only the first term, mishandling a negative sign, or collecting terms that are not alike. The reliable solution is simple: multiply every term, write each product clearly, and simplify only after the brackets have disappeared.

Imagine a student checking a marked question. Their method looks almost right, but the answer is wrong. That is frustrating, yet useful. Expanding brackets mistakes are rarely random. Once you can name each error, you can build a habit that prevents it.

Your expanding brackets checklist

Use this short process every time:

Identify the term or bracket multiplying everything inside.
Multiply it by every term in the bracket.
Write each product, including its sign.
Expand all brackets before collecting like terms.
Check negative multiplication separately.
If there are two brackets, make sure every term in the first bracket multiplies every term in the second.

The central idea is the distributive law:

a (b + c) = ab + a c

The multiplier outside the bracket belongs to both terms. It cannot stop after the first one.

Mistake: multiplying only the first term

Suppose the question is to expand:

3 (x + 5)

A common incorrect answer is:

3 x + 5

Why it happens

The student sees the multiplication beside $x$ , completes $3×x3\times x$ , and then copies the $5$ . But the bracket means that $3$ multiplies the entire expression inside it.

Correct method

Write both multiplications:

3 (x + 5)

=(3×x)+(3×5)=(3\times x)+(3\times 5)

= 3 x + 15

A quick visual habit helps: draw one small line from the outside term to each term inside the bracket. If there are two terms inside, there must be two multiplications.

You can review this idea through the Expanding and Factorising revision lesson, which explains why brackets represent multiplication.

Mistake: losing a negative sign

Negative multipliers create many expanding brackets mistakes because two decisions are happening at once. You must multiply the terms and determine the signs.

Expand:

- 4 (x - 3)

An incorrect answer might be:

- 4 x - 12

Why it happens

The first product is handled correctly, but the student treats a negative multiplied by a negative as another negative.

Remember:

−×−=+-\times -=+

Correct method

Deal with each product separately:

- 4 (x - 3)

=(−4×x)+(−4×−3)=(-4\times x)+(-4\times -3)

= - 4 x + 12

Do not try to hold both products in your head. Written working feels slower, but it often saves the time that would otherwise be spent finding an invisible sign error.

A stick-figure student's brain relaxes after signs are written down instead of held in their head

Mistake: confusing subtraction before a bracket

Now consider:

7 - (2 x + 3)

A student may write:

7 - 2 x + 3

Why it happens

The subtraction sign affects the whole bracket, not just its first term. One way to make that visible is to treat the sign as multiplication by $- 1$ :

7 - (2 x + 3) = 7 + (- 1) (2 x + 3)

Correct method

Multiply every term inside the bracket by $- 1$ :

7 - (2 x + 3)

= 7 - 2 x - 3

Now collect the constant terms:

= 4 - 2 x

A useful check is to ask, “Did every sign inside the subtracted bracket change?” Here, $+ 2 x$ becomes $- 2 x$ , while $+ 3$ becomes $- 3$ .

You now have the core method in hand; use the Maths Genie expanding and factorising lesson and its Question Bank to turn each correction into a repeatable habit.

Mistake: collecting terms that are not alike

Expanding and simplifying are connected, but they are not the same step.

Expand and simplify:

5 (x + 2) + 3 x

A student might incorrectly give:

8 x + 10 x

Why it happens

After expanding $5 (x + 2)$ , the student tries to combine $10$ with $3 x$ . But $10$ is a constant and $3 x$ is an $x$ term. They are not like terms.

Correct method

Expand first:

5 (x + 2) + 3 x = 5 x + 10 + 3 x

Then collect only the $x$ terms:

5 x + 3 x = 8 x

Therefore:

5 (x + 2) + 3 x = 8 x + 10

Terms are alike when their variable parts match exactly. For example, $5 x$ and $3 x$ are like terms, but $5 x$ and $3x^2$ are not.

Mistake: missing products in double brackets

On higher tier papers, you may need to expand two brackets. Every term in the first bracket must multiply every term in the second.

Expand:

(x + 4) (x + 2)

An incomplete answer is:

x^2+8

Why it happens

The student multiplies the first terms and the last terms, but misses the two cross-products. There should be four products before simplification.

Correct method

Multiply $x$ by both terms in the second bracket:

x(x+2)=x^2+2x

Then multiply $4$ by both terms:

4 (x + 2) = 4 x + 8

Put the results together:

x^2+2x+4x+8

Collect the like terms:

x^2+6x+8

Writing the middle line matters. It proves that all four products have been considered and makes any mistake easier to locate.

Mistake: mishandling two negative terms

Expand:

(x - 5) (x - 3)

A common incorrect answer is:

x^2-8x-15

Why it happens

The middle terms are negative, but the final product comes from multiplying two negative numbers. That product must be positive.

Correct method

List all four products:

x×x=x2x\times x=x^2

x×(−3)=−3xx\times(-3)=-3x

(−5)×x=−5x(-5)\times x=-5x

(−5)×(−3)=15(-5)\times(-3)=15

Now combine them:

x^2-3x-5x+15

x^2-8x+15

Notice how the sign check is separated from collecting like terms. Trying to perform every step at once makes an otherwise manageable question fragile.

How to check an expanded expression

Substitution provides a strong check. It does not replace the algebra, but it can reveal whether an expansion is wrong.

For example, consider:

2 (x + 3) = 2 x + 6

Choose $x = 1$ . The original expression gives:

2 (1 + 3) = 8

The expanded expression also gives:

2 (1) + 6 = 8

Because the values agree, the expansion passes this check. If the values were different, the expressions could not be equivalent.

For double brackets, also inspect the structure of your result. Multiplying an $x$ term by another $x$ term should produce an $x^2$ term. The constant term comes from multiplying the constants.

Exam-style practice

Try these without looking back at the examples. Show every multiplication and simplify where possible.

Expand $6 (x + 4)$ .
Expand $- 3 (x - 7)$ .
Expand and simplify $4 (x + 5) + 2 x$ .
Expand and simplify $9 - (3 x + 2)$ .
Expand $(x + 3) (x + 7)$ .
Expand $(x - 4) (x - 6)$ .
Find and correct the error: $5 (2 x - 3) = 10 x - 3$ .
Find and correct the error: $x-2)(x+5)=x^2+10$ .

Answers

$6 x + 24$
$- 3 x + 21$
$6 x + 20$
$7 - 3 x$
$x^2+10x+21$
$x^2-10x+24$
The $- 3$ must also be multiplied by $5$ , so the answer is $10 x - 15$ .
Four products are required, so the answer is $x^2+3x-10$ .

After checking these, work through the Expanding and Factorising exam booklet. It provides further questions with answers, while the main topic page brings the lesson and practice together. If you later meet three multiplied brackets, the Expanding Triple Brackets revision guide develops the same bracket-by-bracket discipline.

Turn corrected errors into secure marks

Knowing why an answer went wrong is different from remembering the correct method under exam pressure. The gap is deliberate practice: multiply every term, write the signs, and simplify only after expanding. Start the Maths Genie expanding and factorising lesson and Question Bank, then correct each missed product before attempting the next question.

A bracket can look harmless. Then one missed multiplication or negative sign changes the whole expression.

Your expanding brackets checklist

Use this short process every time:

Identify the term or bracket multiplying everything inside.
Multiply it by every term in the bracket.
Write each product, including its sign.
Expand all brackets before collecting like terms.
Check negative multiplication separately.
If there are two brackets, make sure every term in the first bracket multiplies every term in the second.

The central idea is the distributive law:

a (b + c) = ab + a c

The multiplier outside the bracket belongs to both terms. It cannot stop after the first one.

Mistake: multiplying only the first term

Suppose the question is to expand:

3 (x + 5)

A common incorrect answer is:

3 x + 5

Why it happens

The student sees the multiplication beside $x$ , completes $3×x3\times x$ , and then copies the $5$ . But the bracket means that $3$ multiplies the entire expression inside it.

Correct method

Write both multiplications:

3 (x + 5)

=(3×x)+(3×5)=(3\times x)+(3\times 5)

= 3 x + 15

A quick visual habit helps: draw one small line from the outside term to each term inside the bracket. If there are two terms inside, there must be two multiplications.

You can review this idea through the Expanding and Factorising revision lesson, which explains why brackets represent multiplication.

Mistake: losing a negative sign

Negative multipliers create many expanding brackets mistakes because two decisions are happening at once. You must multiply the terms and determine the signs.

Expand:

- 4 (x - 3)

An incorrect answer might be:

- 4 x - 12

Why it happens

The first product is handled correctly, but the student treats a negative multiplied by a negative as another negative.

Remember:

−×−=+-\times -=+

Correct method

Deal with each product separately:

- 4 (x - 3)

=(−4×x)+(−4×−3)=(-4\times x)+(-4\times -3)

= - 4 x + 12

Do not try to hold both products in your head. Written working feels slower, but it often saves the time that would otherwise be spent finding an invisible sign error.

A stick-figure student's brain relaxes after signs are written down instead of held in their head

Mistake: confusing subtraction before a bracket

Now consider:

7 - (2 x + 3)

A student may write:

7 - 2 x + 3

Why it happens

The subtraction sign affects the whole bracket, not just its first term. One way to make that visible is to treat the sign as multiplication by $- 1$ :

7 - (2 x + 3) = 7 + (- 1) (2 x + 3)

Correct method

Multiply every term inside the bracket by $- 1$ :

7 - (2 x + 3)

= 7 - 2 x - 3

Now collect the constant terms:

= 4 - 2 x

A useful check is to ask, “Did every sign inside the subtracted bracket change?” Here, $+ 2 x$ becomes $- 2 x$ , while $+ 3$ becomes $- 3$ .

You now have the core method in hand; use the Maths Genie expanding and factorising lesson and its Question Bank to turn each correction into a repeatable habit.

Mistake: collecting terms that are not alike

Expanding and simplifying are connected, but they are not the same step.

Expand and simplify:

5 (x + 2) + 3 x

A student might incorrectly give:

8 x + 10 x

Why it happens

After expanding $5 (x + 2)$ , the student tries to combine $10$ with $3 x$ . But $10$ is a constant and $3 x$ is an $x$ term. They are not like terms.

Correct method

Expand first:

5 (x + 2) + 3 x = 5 x + 10 + 3 x

Then collect only the $x$ terms:

5 x + 3 x = 8 x

Therefore:

5 (x + 2) + 3 x = 8 x + 10

Terms are alike when their variable parts match exactly. For example, $5 x$ and $3 x$ are like terms, but $5 x$ and $3x^2$ are not.

Mistake: missing products in double brackets

On higher tier papers, you may need to expand two brackets. Every term in the first bracket must multiply every term in the second.

Expand:

(x + 4) (x + 2)

An incomplete answer is:

x^2+8

Why it happens

The student multiplies the first terms and the last terms, but misses the two cross-products. There should be four products before simplification.

Correct method

Multiply $x$ by both terms in the second bracket:

x(x+2)=x^2+2x

Then multiply $4$ by both terms:

4 (x + 2) = 4 x + 8

Put the results together:

x^2+2x+4x+8

Collect the like terms:

x^2+6x+8

Writing the middle line matters. It proves that all four products have been considered and makes any mistake easier to locate.

Mistake: mishandling two negative terms

Expand:

(x - 5) (x - 3)

A common incorrect answer is:

x^2-8x-15

Why it happens

The middle terms are negative, but the final product comes from multiplying two negative numbers. That product must be positive.

Correct method

List all four products:

x×x=x2x\times x=x^2

x×(−3)=−3xx\times(-3)=-3x

(−5)×x=−5x(-5)\times x=-5x

(−5)×(−3)=15(-5)\times(-3)=15

Now combine them:

x^2-3x-5x+15

x^2-8x+15

Notice how the sign check is separated from collecting like terms. Trying to perform every step at once makes an otherwise manageable question fragile.

How to check an expanded expression

Substitution provides a strong check. It does not replace the algebra, but it can reveal whether an expansion is wrong.

For example, consider:

2 (x + 3) = 2 x + 6

Choose $x = 1$ . The original expression gives:

2 (1 + 3) = 8

The expanded expression also gives:

2 (1) + 6 = 8

Because the values agree, the expansion passes this check. If the values were different, the expressions could not be equivalent.

For double brackets, also inspect the structure of your result. Multiplying an $x$ term by another $x$ term should produce an $x^2$ term. The constant term comes from multiplying the constants.

Exam-style practice

Try these without looking back at the examples. Show every multiplication and simplify where possible.

Expand $6 (x + 4)$ .
Expand $- 3 (x - 7)$ .
Expand and simplify $4 (x + 5) + 2 x$ .
Expand and simplify $9 - (3 x + 2)$ .
Expand $(x + 3) (x + 7)$ .
Expand $(x - 4) (x - 6)$ .
Find and correct the error: $5 (2 x - 3) = 10 x - 3$ .
Find and correct the error: $x-2)(x+5)=x^2+10$ .

Answers

$6 x + 24$
$- 3 x + 21$
$6 x + 20$
$7 - 3 x$
$x^2+10x+21$
$x^2-10x+24$
The $- 3$ must also be multiplied by $5$ , so the answer is $10 x - 15$ .
Four products are required, so the answer is $x^2+3x-10$ .

Your expanding brackets checklist

Mistake: multiplying only the first term

Why it happens

Correct method

Mistake: losing a negative sign

Why it happens

Correct method

Mistake: confusing subtraction before a bracket

Why it happens

Correct method

Mistake: collecting terms that are not alike

Why it happens

Correct method

Mistake: missing products in double brackets

Why it happens

Correct method

Mistake: mishandling two negative terms

Why it happens

Correct method

How to check an expanded expression

Exam-style practice

Answers

Turn corrected errors into secure marks

Frequently Asked Questions

What is the most common mistake when expanding brackets?

What is the most common mistake when expanding brackets?

How do I expand brackets with a negative number outside?

How do I expand brackets with a negative number outside?

How many products should double brackets create?

How many products should double brackets create?

Can I check an expansion by substitution?

Can I check an expansion by substitution?

Should I collect like terms while expanding brackets?

Should I collect like terms while expanding brackets?

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Your expanding brackets checklist

Mistake: multiplying only the first term

Why it happens

Correct method

Mistake: losing a negative sign

Why it happens

Correct method

Mistake: confusing subtraction before a bracket

Why it happens

Correct method

Mistake: collecting terms that are not alike

Why it happens

Correct method

Mistake: missing products in double brackets

Why it happens

Correct method

Mistake: mishandling two negative terms

Why it happens

Correct method

How to check an expanded expression

Exam-style practice

Answers

Turn corrected errors into secure marks

Frequently Asked Questions

What is the most common mistake when expanding brackets?

Ready to breeze through your GCSEs?

Ready to breeze through your GCSEs?