Q. 6.12 - Intermediate Algebra

Question

Factor: $8n(n-4)+5(n-4)$.

Step-by-Step Solution

Answer

The factored form is $\begin{array}{rcl}& & (n-4)(8n+5)\end{array}$.

Step 1. Given Information

The given expression is $8n(n-4)+5(n-4)$.

Step 2. Rewrite the given expression

• Express each of the term of the given expression as a product of GCF, $n-4$.

$(n-4)·8n+(n-4)·5$

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

$(n-4)·8n+(n-4)·5=(n-4)(8n+5)$

Step 3. Check

• Multiply the obtained factors.

$\begin{array}{rcl}(n-4)(8n+5)& =& (n-4)·8n+(n-4)·5\\ & =& 8n(n-4)+5(n-4)\end{array}$

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