Chapter 7.1, Problem 21IP

To determine

To simplify the expression $\left(b+4\right)12$ .

Answer to Problem 21IP

  $12b+48$

Explanation of Solution

Given information:

The expression, $\left(b+4\right)12$

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: $a\left(b+c\right)=a\cdot b+a\cdot c$
• Right Distributive property: $\left(a\pm b\right)c=a\cdot c\pm b\cdot c$
• Exponent property: $x^n\cdot x^m=x^{n+m}$

Calculation:

In order to simplify the given expression $\left(b+4\right)12$ , first use the distributive property to expand the parenthesis and then simplify further by using the exponent property as shown below

  $\begin{array}{c}\left(b+4\right)12=\left(b+4\right)12\\ =b\left(12\right)+4\left(12\right)\\ =12b+48\end{array}$

Thus, the given expression simplifies to $12b+48$ .