Expansion of Simple Expressions

To expand the bracket means to remove the bracket. To do this, multiply each term inside the bracket by the term outside the bracket. Then simplify by adding the like terms together.

Same signs give a positive result:

Different signs give a negative result:

Worked Example 5.1.1:

Expand the following:

a. 3(a + b) 
b. -8(3x  – y)
c. 5(6 – z)
d. -4(m + n)
e. \( \scriptsize 4x \left( 2y \: – \: z \right) \)
f. 3a(x – 4y)

Solution

a. 3(a + b) 

=  3a  + 3b

b. -8(3x  – y)

=  -24x + 8y

c. 5(6 – z)

= 30 – 5z

d. -4(m + n)

= -4m – 4n

e. \( \scriptsize 4x \left( 2y \: – \: z \right) \\ = \scriptsize 4x \left( 2y \right) \: – \: 4x \left(z \right) \\ = \scriptsize 8xy \; – \; 4xz \)

f. 3a(x – 4y)

= 3ax – 12ay