Factorising Linear Expressions

Factorising is the opposite of expanding. When we factorise we are putting an expression into a bracket. We find the largest term we can divide out from all terms and put that outside the bracket.

You could factorise just with numbers.

$$15+20$$

To factorise this expression, you look for common factors in the terms. Both are in the 5 times table.

$$15+20=5(3+4)$$

How to factorise

$$6x+12$$

Identify the common factor. 6x and 12 can both be divided by 6. 6 will be outside the bracket.

$$6()$$

Divide 6x and 12 by 6 to find our terms inside the bracket.

$$6(x+2)$$

Harder factorising

$$14ab+21a$$

Identify the common factor. 14ab and 21a can both be divided by 7, but also by a. 7a will be outside the bracket.

$$7a()$$

Divide 14ab and 21a by 7a to find our terms inside the bracket.

$$7a(2b+3)$$