Math 40
Prealgebra
Section 3.2 – Evaluating Algebraic Expressions
3.2 Evaluating Algebraic Expressions
Tips for Evaluating Algebraic Expressions
1) Replace all variables with open parentheses, ( ).
2) Substitute the given values for each variable into the corresponding parentheses.
3) Simplify the expression using Order of Operations.
Review: Order of Operations
1) Perform all operations inside the grouping symbols. Start with the innermost
grouping and perform all operations inside until you are left with a single
number.
2) Evaluate any exponents in the expression.
3) Moving from left to right, perform any multiplications or divisions in the
order in which they appear.
4) Moving from left to right, perform any additions or subtractions in the order
in which they appear.
Example 1: Evaluate the expression, x 2  2 xy  y 2 , for x  3 and y  2 .
Solution:
x 2  2 xy  y 2  
  2      
2
2
  3   2  3  2    2 
2
2
9

4
9 2  3  2   4
12

9
 12
4
 9  12  4
 25
You Try It 1: If x  2 and y  1 , evaluate x 3  y 3 .
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2015 Worrel
Math 40
Prealgebra
Section 3.2 – Evaluating Algebraic Expressions
Example 2: Evaluate the expression,  a  b  , for x  3 and y  2 .
2
Solution:
a  b
2
 
   
2


   3    5  


 3 5  8 
 8
2
2
 64
You Try It 2: If a  3 and b  5 , evaluate a2  b2 .
Example 3: Evaluate the expression, a  b , for a  5 and b  7 .
Solution:
  
  5    7 
ab 
5
7
 5  7
 2
You Try It 3: If a  5 and b  7 , evaluate 2 a  3 b .
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2015 Worrel
Math 40
Prealgebra
Section 3.2 – Evaluating Algebraic Expressions
Example 4: Evaluate the expression, a  b , for a  5 and b  7 .
Solution:
a b 
  
  5    7 
5  7  12
 12
 12
You Try It 4: If a  5 and b  7 , evaluate 2a  3b .
Example 5: Evaluate the expression,
Solution:
ad  bc
, for a  5, b  3, c  2, and d  4 .
ab
ad  bc 

ab
     
  
 5  4    3 2 

 5    3 
We will simplify the top and bottom separately,
Top:  5  4    3  2   20   6   20  6  14
20
6
6
 5    3  2
 5  4    3 2   Top  14  7
Bottom
2
 5    3 
Bottom:
So,
You Try It 5: If a  7, b  3, c  15, and d  14 , evaluate
a 2  b2
.
cd
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2015 Worrel
Math 40
Prealgebra
Section 3.2 – Evaluating Algebraic Expressions
Example 6:
H
The volume of a rectangular prism, shown to the left, is given by the formula,
V  LWH
where L is the length, W is the width, and H is the height.
W
L
Find the volume of a rectangular prism having length of 12 feet, width of 4 feet, and height of 6
feet.
Solution:
V  LWH

  
 12 ft  4 ft  6 ft 
 288 ft 3 or 288 cubic feet
You Try It 6: The surface area of the rectangular prism pictured above is given by the formula,
S  2 WH  LH  LW 
If L  12 feet, W  4 feet, and H  6 feet , calculate the surface area.
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2015 Worrel