4.2Evaluating Algebraic Expressions

Evaluating an expression means finding its numerical value when specific values are substituted for the variables.

Substitution with two variables

Given $\displaystyle a = 4$ and $\displaystyle b = -7$ , evaluate $\displaystyle 2a^2 - 3b$ .

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\displaystyle 2a^2 - 3b

\displaystyle = 2(4)^2 - 3(-7)

\displaystyle = 2(16) - (-21)

\displaystyle = 32 + 21

\displaystyle = 53

Given $\displaystyle p = -6$ and $\displaystyle q = 4$ , evaluate $\displaystyle \frac{p^2 + q}{2q - p}$ .

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\displaystyle \frac{p^2 + q}{2q - p}

\displaystyle = \frac{(-6)^2 + 4}{2(4) - (-6)}

\displaystyle = \frac{36 + 4}{8 + 6}

\displaystyle = \frac{40}{14}

\displaystyle = \frac{20}{7}

Now you try

If $x = -3$ and $y = 2$ , evaluate $\frac{2y}{3x}$ .

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\displaystyle \frac{2y}{3x}

\displaystyle = \frac{2(2)}{3(-3)}

\displaystyle = -\frac{4}{9}

\displaystyle = -\frac{4}{9}

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