# At a Glance - Evaluating Expressions by Substitution

Remember that a variable is like an empty box that is waiting for a number. It is a box, and it waits patiently. 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 Problems

1. Substitute 3 for *x* in the expression 4*x* + 5. 4*x* + 5 is the same as 4 · ☐ + 5, so write 3 in the box: 4 · [ 3 ] + 5.

To substitute a value for a variable, replace every copy of the variable with the value enclosed in parentheses.

2. Substitute 4 for *y* in the expression 2*y* + *y*^{2}. Replace every occurrence of *y* with (4); 2(4) + (4)^{2}. 4ou see? What did 4ou say? We can stop now? Oh. Thank 4ou.

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

**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?

### Sample Problem

If we forget the parentheses when substituting - 4 for y in the expression 2*y* + *y*^{2}, we find that 2 - 4 + - 4^{2}. This step gives us - 2 - 16 = - 18, which is completely wrong! Not just a little wrong, which would be bad enough, but *completely* wrong!

#### Example 1

Evaluate the expression 4 |

#### Example 2

Evaluate the expression 2 |

#### Example 3

If |

#### Exercise 1

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

#### Exercise 2

Evaluate for *x* = 10.

#### Exercise 3

Evaluate 4*x*^{2} for *x* = - 1.

#### Exercise 4

Evaluate 5*y* - 3*y*^{2} for *y *= - 2.

#### Exercise 5

Evaluate *z*^{3 }- 18 + *z* for *z* = - 2.

#### Exercise 6

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

#### Exercise 7

Evaluate *b*^{2} - 4*ac* for *a* = 1, *b* = 3 and *c* = - 2.