Lesson 6: Expanding and Simplifying

Objective

At the end of this lesson, students should be able to

• Expand products of algebraic expressions and simplify them.

Sometimes it is necessary to simplify algebraic expressions after expansion. You can simplify by collecting like terms.

Example 1

Expand and simplify 3 (x – 4) + 2 (4 – x).

Solution

3 (x – 4) + 2 (4 – x)

Expand the first bracket and then the second bracket.

3x – 12 + 8 – 2x

Collect like terms and simplify

= 3x – 2x + 8 – 12

= x – 4

Example 2

Expand and simplify 2 (6p + 7q) – 3 (2p  – 5q)

Solution

2 (6p + 7q) – 3 (2p – 5q)

Collect like terms and simplify

= 12p + 14q – 6p + 15q

= 12p – 6p +14q + 15q

= 6p + 29q

Example 3

Expand and simplify 6s (2s + 7t) – 2s (5s – 2t)

Solution

6s (2s + 7t) – 2s (5s – 2t)

12s² + 42st – 10s² + 4st

Collect like terms and simplify

= 12s² – 10s² + 42st + 4st

= 2s²+ 46st