Factorising reverses expansion: a sum becomes a product. Extract the greatest common numerical factor and every common letter factor. Expanding the result checks the original expression. Example 6x2y-9xy2=3xy(2x-3y). Both terms contain 3xy; each term inside the bracket is what remains after division by that factor. Grouping creates a common bracket: ax+bx+2ay+2by=x(a+b)+2y(a+b) =(a+b)(x+2y). The bracket is one factor, just as a letter can be one factor. Stop only when no further common factor remains.

Factorising reverses expansion: a sum becomes a product. Extract the greatest common numerical factor and every common letter factor. Expanding the result checks the original expression.

\(6x^2y-9xy^2=3xy(2x-3y)\). Both terms contain \(3xy\); each term inside the bracket is what remains after division by that factor.

Grouping creates a common bracket: \(\begin{aligned}ax+bx+2ay+2by&=x(a+b)+2y(a+b)\\&=(a+b)(x+2y).\end{aligned}\)

The bracket is one factor, just as a letter can be one factor. Stop only when no further common factor remains.

Common factors and grouping

Common factors and grouping