n $7x$.","back":"A coefficient is the number multiplying a variable, such as the 7 in $7x$.","points":null},{"id":"94224e4f-a9ad-49be-af9a-3e48cad23c79","cardType":"basic","front":"Simplify the term $-3x \\cdot 5x$.","back":"$$-15x^2$","points":1},{"id":"01f3bc73-ea2f-42a6-ab52-eb35a514d677","cardType":"basic","front":"What does it mean to expand an expression?","back":"To remove brackets by multiplying out every term.","points":1},{"id":"1cf36a8c-0a50-4022-ba86-832878b912e8","cardType":"cloze","front":"When expanding two brackets, you should produce [ ] initial products before simplifying.","back":"When expanding two brackets, you should produce four initial products before simplifying.","points":null},{"id":"97b49594-b5f5-4a25-8b0c-f0eb1d8252fe","cardType":"basic","front":"Expand and simplify $(x + 5)(x - 2)$.","back":"$$x^2 + 3x - 10$","points":2},{"id":"fc2f28f9-f57e-4c15-b1ed-1ef8662c5ad4","cardType":"basic","front":"Expand and simplify $(3p - 4)(p - 6)$.","back":"$$3p^2 - 22p + 24$","points":2},{"id":"b6e891e7-3fd1-443a-9e27-9039ff3bddbb","cardType":"cloze","front":"The expression $(a - 5)^2$ is equivalent to the expanded form $\\text{[...]}$.","back":"The expression $(a - 5)^2$ is equivalent to the expanded form $\\boxed{(a - 5)(a - 5)}$.","points":null},{"id":"fd4c12df-b835-4673-9337-3103f9143932","cardType":"basic","front":"Expand and simplify $(y - 8)^2$.","back":"$$y^2 - 16y + 64$","points":2},{"id":"cb9ff9c1-00b7-4a1f-a9f8-e9633896858c","cardType":"basic","front":"Why is $(y - 8)^2$ not simply $y^2 + 64$?","back":"The expansion produces a middle term ($-16y$) because every term in the first bracket multiplies every term in the second.","points":2},{"id":"d6f65e42-ef9d-4578-8a32-4d206b78f40e","cardType":"basic","front":"When factorising $x^2 + bx + c$, what two requirements must the numbers in the brackets meet?","back":"

Multiply to give $c$
Add to give $b$

","points":2},{"id":"820b1895-b775-428c-a814-3d5e9ba44f26","cardType":"basic","front":"Factorise $x^2 + 11x + 24$.","back":"$$(x + 3)(x + 8)$","points":2},{"id":"3c12b89a-4871-41f0-83bb-424014bb82ac","cardType":"cloze","front":"If a quadratic has a positive final number and a negative middle term, the signs in the brackets are [ ].","back":"If a quadratic has a positive final number and a negative middle term, the signs in the brackets are both negative.","points":null},{"id":"e2f9435c-dc0f-4e09-8954-a29ef68a4613","cardType":"cloze","front":"If a quadratic has a [ ] final number, the signs in the brackets must be different (one positive, one negative).","back":"If a quadratic has a negative final number, the signs in the brackets must be different (one positive, one negative).","points":null},{"id":"4db8bef1-d281-4858-9df8-3050224f8512","cardType":"basic","front":"Factorise $x^2 - 9x + 20$.","back":"$$(x - 4)(x - 5)$","points":2},{"id":"28a90d5c-264d-4487-9ab4-19a331c9d638","cardType":"basic","front":"Factorise $x^2 + 2x - 35$.","back":"$$(x + 7)(x - 5)$","points":2},{"id":"7e77951a-a3fe-4429-83a3-e2a752a74f78","cardType":"basic","front":"State the general factorised form for the difference of two squares, $x^2 - a^2$.","back":"$$(x + a)(x - a)$","points":1},{"id":"df974ecf-2c94-41f7-8886-3546e619a02f","cardType":"basic","front":"Factorise $x^2 - 64$.","back":"$$(x + 8)(x - 8)$","points":1},{"id":"190f50df-928d-4622-ad1f-bb810b50e165","cardType":"cloze","front":"The \"difference of two squares\" rule [ ] apply to expressions with an addition sign, such as $x^2 + 64$.","back":"The \"difference of two squares\" rule does not

Expanding and Factorising Quadratics Flashcards

Expanding and Factorising Quadratics Flashcards

Expanding and Factorising Quadratics Flashcards

Expanding and Factorising Quadratics Flashcards