Back to Course

## JSS1: MATHEMATICS - 2ND TERM

0% Complete
0/0 Steps

#### Quizzes

Lesson 3, Topic 4
In Progress

# Expanding Brackets or Multiplying out Brackets

Lesson Progress
0% Complete

To expand a bracket means to multiply each term in the bracket by the expression outside the bracket.

For example:  a(x  +  y)  means $$\scriptsize a \: \times \: x \: + \: a \; \times \: y \\ = \scriptsize ax \: + \: ay$$

Also a(x –  y )  =   $$\scriptsize a \; \times \; x \; – \; a \; \times \; y \\ = \scriptsize ax \; – \; ay$$

The equation can also be written like this

(x   +   y) a  =   xa   +   ya

(x   –  y) a   =   xa   –  ya

### Example:

Expand the brackets in the following:

i. $$\scriptsize 5(x \: + \: y)$$
ii. $$\scriptsize 3(x \: + \: 2y)$$
iii. $$\scriptsize 10(p \; – \: q \; – \: r)$$
iv. $$\scriptsize – (3y \; – \: 4z)$$
v. $$\scriptsize 3a \: + \: (4y \; – \: 2a)$$

Solution:

i. $$\scriptsize 5(x \: + \: y)$$

= $$\scriptsize 5 \: \times \: x \: + \: 5 \: \times \: y \\ = \scriptsize 5x \: + \: 5y$$

ii. $$\scriptsize 3(x \: + \: 2y)$$

$$\scriptsize = 3 \: \times \: x \: + \: 3 \: \times \: 2y$$

$$\scriptsize= 3x \: + \: 6y$$

iii. $$\scriptsize 10(p \; – \: q \; – \: r)$$

$$\scriptsize = 10 \: \times \: p \; – \: 10 \: \times \: q \; – \: 10 \: \times \: r$$

$$\scriptsize = 10p \; – \: 10q \; – \: 10r$$

iv. $$\scriptsize – (3y \; – \: 4z)$$

Open the brackets

Note: $$\scriptsize – \: \times \: – \: = +$$

$$\scriptsize = 3y \: + \: 4z$$

v. $$\scriptsize 3a \: + \: (4y \; – \: 2a)$$

Open the brackets

= $$\scriptsize 3a \: + \: 4y \; – \: 2a$$

Collect like terms

= $$\scriptsize 3a \; – \: 2a \: + \: 4y$$

= $$\scriptsize a \: + \: 4y$$