# 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

Unit 1 Lesson 6: Exercise 1

Expand and simplify the following:

1. 2x – 3 (2x + 4)                    6)  5y – 3y (y +2)
2. 8x – 5 (x + 5)                       7)  7y (y + 4) + y2 + 2
3. 4 (x – 5) – 6                        8) 3 (y – 4) + 2(4 – y)
4. 5 (3x – 2y)+ 8y                   9) 6 (x +3) – 4 (x – 1)
5. 6x – 3(2x – 1)                     10) 5 (y – 8)- 4(y -7)

1) – 4x – 12 6) – y – 3y2
2) 3x – 25 7) 8y2 + 28y + 2
3) 4x – 26 8) y – 4
4) 15x – 2y 9) 2x + 2z
5) 3 10) y – 12

Unit 1 Lesson 6: Exercise 2

Expand and simplify the following:

1. 3x (x + 2) – 2 (x2 – 1)
2. 7y (x – 2z) – z (2y – 3)
3. ½ (4x + 6) + 1/3 (9x + 3)
4. ¾ (8x + 6y) + ¼ (2x – 12)
5. 3x2 (2x – 1) + 4x3
6. 3 (5x + 2y) – 6(2x – 3y)
7. x/7 (14x – 21y) – x/2 (4x – 6y)
8. 2/3 (6x – 9y) + 1/3(9x + 6y)
9. 1/5 (15x + 10y) + 3/10 (5x – 5y)
10. 1/8 (6x – 12y) + ½ (3x – 2y)

1) x2 + 6x + 2 6) 3x + 24y
2) 7xy – 16yz + 3z 7) 0
3) 5x + 4 8) 7x – 4y
4) 13/2x + 9/2y – 3 9) 9/2x + ½ y
5) 10×3 – 3×2 10) 9/4x – 5/2y

Lesson Content
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