Chapter 4.6, Problem 41S

To determine

To write: an equivalent algebraic expression using Distributive property

Answer to Problem 41S

An equivalent algebraic expression for expression is $\text{18+2}p$ .

Explanation of Solution

Given: $-2(-9-p)$

Calculation:

According to the distributive property,

  $a(b+c)=ab+ac$

Compare the expression $-2(-9-p)\text{ to 18+2}p$ .

  $a=-2,b=-9\text{ and }c=-p$

Apply the distributive property,

  $\begin{array}{l}-2(-9-p)=-2(-9)-2(-p)\\ \text{ =2(9)}+2(p)\\ =\text{18+2}p\end{array}$

Conclusion: Hence, an equivalent algebraic expression for expressionis $\text{18+2}p$ ..