Chapter 8.3, Problem 47CCR

To determine

Expression $-2\left(-9-p\right)$ as equivalent algebraic expression

Answer to Problem 47CCR

An equivalent algebraic expression is $18+2p$

Explanation of Solution

Given information:

The expression, $-2\left(-9-p\right)$

Concept used:

The distributive property of binomials (FOIL): $\left(a+b\right)\left(c+d\right)=a\cdot c+a\cdot d+b\cdot c+b\cdot d$

Left distributive property: $a\left(b+c\right)=a\cdot b+a\cdot c$

Exponent property: $x^n\cdot x^m=x^{n+m}$

Calculation:

In order to simplify the given expression, use the left distributive property and simplify as shown below

  $\begin{array}{c}-2\left(-9-p\right)\\ =\left(-2\right)\cdot \left(-9\right)+\left(-2\right)\cdot \left(-p\right)\\ =18+2p\end{array}$

Thus, the given expression as an equivalent algebraic expression is $18+2p$