Lesson 2: Evaluating more complex Algebraic Expressions

Objectives

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

• Evaluate more complex algebraic expressions.

Example 1

Given that p=4, q=-2 and r=3, find the values of the following expressions:

1. 3(p + q) – 2(q + r)

2. (2p + r)² – q²

3. (2p + 3q + 4r)²

Solution

1. 3(p + q) – 2(q + r) = 3(4 + (-2)) – 2(-2 +3)

= 3(4 – 2) – 2(-2 +3)

= 3(2) – 2(1)

= 6 – 2

= 4

2. (2p + r)² – q² = (2(4) + 3)² – (-2)²

= (8 + 3)² – 4

= (11)² – 4

= 121 – 4

= 117

3. (2p + 3q + 4r)²  = (2(4) + 3(-2) + 4(3))²

= (8 – 6 + 12)²

= (14)²

= 196

Example 2

If a = 2.4,  b =  1.9,  c = 1.1  and  d = 0.6, find correct to one decimal place, the values of the following expressions: (You may use a calculator)

1. d²

2. c² + d²

Solution 

1. d² = d × d

= 0.6 × 0.6 = 0.36

≈ 0.4  (≈ means Approximately)

2. c² + d² = (1.1)² + (0.6)²

= 1.21 + 0.36

= 1.57

≈ 1.6