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Algebraic Expressions

Algebraic Expressions

At a Glance - Evaluating Expressions by Substitution


Remember that a variable is like an empty box that's waiting for a number. Have you ever seen a box wait? Those things have unbelievable staying power.

We call it substitution when we put a number into the box.

Sample Problem

What's the value of 4x + 5 when x = 3?

Let's break it down: 4x + 5 is the same as 4 · ☐ + 5, so write 3 in the box:

4(3) + 5

After substituting values for the variables in an expression, we can evaluate the expression by working out the arithmetic.

4(3) + 5 =
12 + 5 = 17

Long story short: to substitute a value for a variable, replace every copy of the variable with the value enclosed in parentheses.

Sample Problem

What's the value of 2yy2 when y = 4?

Here we go: replace every occurrence of y with 4:

2(4) + (4)2

4ou see? What did 4ou say? We can stop now? Oh. Thank 4ou.

2(4) + (4)2 =
8 + 16 = 24

Be Careful: Make sure to put parentheses around values when substituting for variables. There can be some mix-ups with negative signs otherwise. We don't want no more mix-ups. Not after that failed bank heist. You hear that, Ira?

Example 1

What's the value of the expression 5x + 11 when x = 3?


Example 2

What's the value of 3y2 + 3y if y = 2?


Example 3

If y = -4, what's the value of the expression 2y + y2?


Exercise 1

Evaluate -3x + 4 for x = -2.


Exercise 2

Evaluate  for x = 10.


Exercise 3

Evaluate 4x2 for x = -1.


Exercise 4

Evaluate 5y – 3y2 for y = -2.


Exercise 5

Evaluate z3 – 18 + z for z = -2.


Exercise 6

Evaluate 4xyz + x + yz for x = 2, y = 3, and z = 5.


Exercise 7

Evaluate b2 – 4ac for a = 1, b = 3 and c = -2.


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