# Factorise algebraic expressions

Lesson

Factorisation is finding common factors (usually the HCF) between all the terms in a long algebraic expression and using them to rewrite the expression as a product of many factors. In some ways it can be thought of as the opposite of expanding brackets as factorisation puts many terms into products of brackets.

One method of factorisation follows the following:

$AB+AC+AD=A\left(B+C+D\right)$AB+AC+AD=A(B+C+D)

where $A$A is the HCF of all the terms, and can be extended to examples with more or less than three terms.

Where there are many different variables involved, just look at each one individually and see what the HCF is between the terms.

#### Examples

##### Question 1

Fill in the spaces to complete the equality:

1. $y^2+5y=y\left(\editable{}+\editable{}\right)$y2+5y=y(+)

##### Question 2

Factorise the following expression:

$pqr+p^2q^2r+p^3q^3r$pqr+p2q2r+p3q3r

##### Question 3

Factorise the following:

$9\left(3x+4\right)+4\left(3x+4\right)$9(3x+4)+4(3x+4)

##### question 4

Factorise the following expression:

$7x\left(x-5\right)+\left(x-5\right)^2+6\left(x-5\right)$7x(x5)+(x5)2+6(x5)