Expanding Brackets or Multiplying out Brackets

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 3.4.1:

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: