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Basic Algebra

Basic Algebra

At a Glance - Evaluating Algebraic Expressions

To evaluate an algebraic expression, just plug numbers into the expression and simplify it.

Don't Forget: you will need your faithful friend PEMDAS (aka Order of Operations).

Here's a video example of math in action. Practice, practice, practice.

 

Example 1

Evaluate the expression when x = 2, y = -3, and z = -1.

2x + 3y - z


Example 2

Find the values of the expression for x = -2, -1, 0, 1, 2

3x^2 + 1

This question is asking us to evaluate the expression for five different values. It may be easiest to do this in chart form.

X3x2 + 1Simplified
-23(-2)2 + 13(-2)2 + 1
3(4) + 1
12 + 1
13
-13(-1)2 + 13(-1)2 + 1
3(1) + 1
3 + 1
4
3(0)2 + 13(0)2 + 1
3(0) + 1
0 + 1
1
13(1)2 + 13(1)2 + 1
3(1) + 1
3 + 1
4
23(2)2 + 13(2)2 +1
3(4) +1
12 + 1
13

Example 3

Which of these values (-2, -1, 0, 1, 2) makes this equation true?

x^4 - 1 = 0

Just like the previous problem, it is probably useful to make a chart.

evaluating an expression 2


Exercise 1

Evaluate the expression 3x2 + 5xy – 2 for x = 3 and y = -2.


Exercise 2

The formula for the surface area of a cone is πrs + πr2, where r is the radius of the base and s is the length of the slant. Find the surface area of a cone with radius 10 cm and a slant of 12 cm (use 3.14 for π).


Exercise 3

Evaluate the expression x3 + x2 + x + 1 for x values equal to -2, -1, 0, 1, 2.


Exercise 4

Which of these values of x (1, 2, 3, 4, 5, 6) make this equation true: x2 – 8x = -12?


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