__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)

12s^{2} + 42st – 10s^{2} + 4st

Collect like terms and simplify

= 12s^{2} – 10s^{2 }+ 42st + 4st

= 2s^{2}+ 46st

__ __

__Unit 1 Lesson 6: Exercise 1__

**Expand and simplify the following:**

- 2x – 3 (2x + 4) 6) 5y – 3y (y +2)
- 8x – 5 (x + 5) 7) 7y (y + 4) + y
^{2}+ 2 - 4 (x – 5) – 6 8) 3 (y – 4) + 2(4 – y)
- 5 (3x – 2y)+ 8y 9) 6 (x +3) – 4 (x – 1)
- 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

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:**

- 3x (x + 2) – 2 (x
^{2}– 1) - 7y (x – 2z) – z (2y – 3)
- ½ (4x + 6) +
^{1}/_{3}(9x + 3) - ¾ (8x + 6y) + ¼ (2x – 12)
- 3x
^{2}(2x – 1) + 4x^{3} - 3 (5x + 2y) – 6(2x – 3y)
^{x}/_{7 }(14x – 21y) –^{x}/_{2}(4x – 6y)^{2}/_{3}(6x – 9y) +^{1}/_{3}(9x + 6y)^{1}/_{5}(15x + 10y) +^{3}/_{10}(5x – 5y)^{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

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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