Download My Math GPS: Elementary Algebra Guided Problem Solving

Algebraic Expressions
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Algebraic Expressions
GPS 38: Evaluating Algebraic Expressions
In many instances, we have expressions into which we must substitute values. In this section, we will learn how
to substitute given values of variables into the given algebraic expressions. This section will test our knowledge
and application of the order of operations. We will see how to do this in the example below.
Problem 38.1
Given 𝑎𝑎 = 2 and 𝑏𝑏 = −1, evaluate the expression given below.
𝑎𝑎2 + 𝑎𝑎𝑎𝑎 + 𝑏𝑏 2
We evaluate this expression by simply substituting the given values into the expression above. In each case, we
must remember to first raise numbers to the power, then multiply and finally, add or subtract.
𝑎𝑎2 + 𝑎𝑎𝑎𝑎 + 𝑏𝑏 2
2
(2) + (2)(−1) + (−1)2
Replace 𝑎𝑎 with 2, and 𝑏𝑏 with −1.
=4−2+1
Remember to raise to the power first.
=2+1
Multiply.
=3
Add the first two terms.
The value of the expression is 𝟑𝟑.

Problem 38.2
Given 𝑎𝑎 = 1 and 𝑏𝑏 = 2, evaluate the expression given below.
𝑎𝑎2 − 𝑎𝑎 + 𝑏𝑏 2
Answer =_____

Problem 38.3
Given 𝑎𝑎 = −2 and 𝑏𝑏 = 3, evaluate the expression given below.
2𝑎𝑎2 𝑏𝑏 − 4𝑎𝑎𝑎𝑎 − 3𝑏𝑏 2
We evaluate this expression by simply substituting the given values into the expression above. In each case, we
must remember to first raise numbers to the power, then multiply and finally, add or subtract.
2𝑎𝑎2 𝑏𝑏 − 4𝑎𝑎𝑎𝑎 − 3𝑏𝑏 2
= 2(−𝟐𝟐)2 (𝟑𝟑) − 4(−𝟐𝟐)(𝟑𝟑) − 3(𝟑𝟑)2
= 2(4)(3) + 24 − 3(9)
= 24 + 24 − 27
= 48 − 27
= 21
The value of the expression is 𝟐𝟐𝟐𝟐.

Replace 𝑎𝑎 with −2, and 𝑏𝑏 with 3.
Remember to raise to the power first.
Multiply.
Add the first two terms.
Subtract.
My Math GPS: Elementary Algebra. Guided Problem Solving by Cornick, Guy, & Puri. 2016 Edition.