Chapter 7.1, Problem 8GP

To determine

To simplify the expression $-6\left(b-5\right)$ .

Answer to Problem 8GP

  $-6b+30$

Explanation of Solution

Given information:

The expression, $-6\left(b-5\right)$

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: $a\left(b+c\right)=a\cdot b+a\cdot c$
• 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 $-6\left(b-5\right)$ , first use the distributive property to expand the parenthesis and then simplify further by using the exponent property as shown below

  $\begin{array}{c}-6\left(b-5\right)=-6\left(b-5\right)\\ =-6\cdot b+\left(-6\right)\cdot \left(-5\right)\\ =-6b+30\end{array}$

Thus, the given expression simplifies to $-6b+30$ .