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Multivariable Expressions Study Guide (page 2)

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Updated on Oct 3, 2011

Evaluating Multivariable Expressions

Now that we know how to simplify multivariable expressions, we can evaluate them. To evaluate a multivariable expression, replace each variable in the expression with its value. As always, remember the order of operations!

Example

What is 5y – 2z when y = 3 and z = –1?

The terms 5y and –2z are unlike, so they cannot be simplified. Replace y with 3 and replace z with –1:

5(3) – 2(–1) = 15 + 2 = 17

Example

What is 3a + 4b – 4a + 3b when a = 5 and b = 6?

First, combine the two a terms and the two b terms:

3a – 4a = –a

4b + 3b = 7b

The expression is now –a + 7b. Replace a with 5 and b with 6:

–5 + 7(6) = –5 + 42 = 37

Example

What is 3(s + 2t) – 6t + 4s when s = –2 and t = 32?

First, use the distributive law to find 3(s + 2t). Multiply 3 by s and multiply 3 by 2t:

3(s + 2t) = 3s + 6t

The expression is now:

3s + 6t – 6t + 4s

Combine the two s terms and the two t terms:

3s + 4s = 7s

6t – 6t = 0

The expression is now just 7s. Replace s with –2. There are no t terms to replace.

7(–2) = –14

The preceding example shows why simplifying an expression can often make evaluating an expression easier. Rather than having to add, subtract, multiply, or divide with 32, the value of t, in the end, the only calculation we had to do after substituting the value of s was to multiply 7 by –2.

Find practice problems and solutions for these concepts at Multivariable Expressions Practice Questions.

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