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 = 2.4b1.9c = 1.1  and  d = 0.6, find correct to one decimal place, the values of the following expressions: (You may use a calculator)

  1. c² + d²

Solution 

  1. d² = d × d

= 0.6 × 0.6 = 0.36

0.4  (≈ means Approximately)

  1. c² + d² = (1.1)² + (0.6

= 1.21 + 0.36

= 1.57

1.6

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