Factorising — Common Factor & Grouping

Simplify algebraic expressions, expand binomial products and factorise monic quadratic expressions.

Always look for a common factor first, before anything else.

Worked example

e.g.

7x(2x-3y) - (3y-2x)

Identify the common factor in each term — recognise the contents of the brackets $7x(2x-3y) - (3y-2x)$
Change the sign in front of one bracket and switch the terms inside $7x(2x-3y) + (2x-3y)$
Write out as a product of the factors $(2x-3y)(7x+1)$

5(x+y) + b(x+y)

Answer

(x+y)(5+b)

x(x+4) - 3(x+4)

Answer

(x+4)(x-3)

x(x-2) + (x-2)

Answer

(x-2)(x+1)

28 - 14x - 2x + x^{2}

Answer

(x-14)(x-2)

2ax - 2ay - 5cx + 5cy

Answer

(x-y)(2a-5c)

4x + 12 - xy - 3y

Answer

(x+3)(4-y)

24x^{3} - 64x^{2} - 21x + 56

Answer

(3x-8)(8x^{2}-7)

8 - 12x - 6x^{3} + 9x^{4}

Answer

(2-3x)(4-3x^{3})