Algebra II (AQA GCSE Further Maths): Flashcards

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Factorising
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Definition of factorising

Writing an algebraic expression as product of factors using brackets

Factorising is reverse of

Expanding brackets

Grouping method: number of terms

Four terms

For x2+bx+cx^2 + bx + c: what must two numbers do?

Multiply to cc, add to bb

Negative constant: factor signs

One positive, one negative

a2b2a^2 - b^2 factorises to

(a+b)(ab)(a + b)(a - b)

Difference of two squares pattern

a2b2a^2 - b^2

'Factorise fully' means

Use multiple steps until no further factorisation possible

First step when factorising

Look for common factors

For ax2+bx+cax^2 + bx + c: find product of

a×ca \times c

How to verify factorising work

Expand back out to check original expression

Terms in difference of two squares must be

Perfect squares

Grouping: after common factors, look for

Common bracket in both groups

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