Question

Factor:$4m(m+3)-7(m+3)$.

Short answer

The factored form is$\begin{array}{rcl}& & (m+3)(4m-7)\end{array}$.

Step-by-step solution

Step 1. Given Information

The given expression is$4m(m+3)-7(m+3)$

Step 2. Rewrite the given expression    

• Express each of the term of the given expression as a product of GCF, $m+3$.

localid="1661475888161" $(m+3)·4m-(m+3)·7$

• Use the reverse distributive property, localid="1661475904769" $ab-ac=a(b-c)$to rewrite the obtained expression.

localid="1661475937561" $(m+3)·4m-(m+3)·7=(m+3)(4m-7)$

Step 3. Check

• Multiply the obtained factors.

$\begin{array}{rcl}(m+3)(4m-7)& =& (m+3)·4m-(m+3)·7\\ & =& 4m(m+3)-7(m+3)\end{array}$

• Since the obtained expression is the same as the given expression, the obtained factors are verified.