Chapter 8.7, Problem 9PPE

To determine

The solution of the given expression.

Answer to Problem 9PPE

The factor of expression $h^2+8h+16$ is $\left(h+4\right)\left(h+4\right)$

Explanation of Solution

Given information:

The expression $h^2+8h+16$

Concept and Formula Used:

The property ${\left(a+b\right)}^2=a^2+2ab+b^2$

Calculation:

The given expression is $h^2+8h+16$

Write the first and last term of the expression as squares and middle term in the form of 2ab

  $h^2+8h+16={\left(h\right)}^2+2\times 4\times h+{\left(4\right)}^2$

Using the property ${\left(a+b\right)}^2=a^2+2ab+b^2$

Therefore

  $\begin{array}{l}{h}^2+8h+16={\left(h+4\right)}^2\\ h^2+8h+16=\left(h+4\right)\left(h+4\right)\end{array}$

Conclusion:

The factor of expression $h^2+8h+16$ is $\left(h+4\right)\left(h+4\right)$