Single brackets: Expanding and factorising

In a nutshell

A number or term can be multiplied by an expression in brackets. e.g. $2x(3x+2y)$ . The term on the outside of the bracket should be multiplied by each term in the expression that is inside the brackets. This is called multiplying out single brackets. Some expressions can be put back into single brackets (factorised), by taking out a common factor from the expression.

Note: Be careful with negative signs inside the bracket, or with a negative term in front of the bracket.

Multiplying out single brackets

To multiply out brackets, multiply the number on the outside with each term on the inside of the bracket. You can use a multiplication grid to help.

Example 1

Multiply out $2(x+3)$ .

Maths; Algebra; KS4 Year 10; Single brackets: Expanding and factorising

Use a multiplication grid to help.

$\times$	$x$	$+3$
$2$	$2x$	$6$

Examples

$3(y+1)$	$= 3y+3$
$2x (x-5)$	$=2x^2 - 10x$
$3a(2b+5t)$	$=6ab+15at$
$-5x(3x-4y)$	$=-15x^2+20xy$
$3b(2c^2+7d-3)$	$=6bc^2+21bd-9b$

Factorise single brackets

To factorise single brackets, think about what is common in all the terms in the expression. This is the common factor. Keep the common factor on the outside of the bracket, and find the expression on the inside of the bracket.

Example 2

Factorise $3x+12$ .

$3x$ and $12$ both have a common factor of $3$ . So take the number $3$ on the outside of the bracket. Then you need $x$ , to multiply with $3$ to get $3x$ , and $+4$ to multiply by $3$ to get $+12$ .

$3x+12 = \underline{3(x+4)}$

You can use a multiplication grid to help.

$\times$	$x$	$+4$
$3$	$3x$	$+12$