Chapter 7.7, Problem 1E

To determine

To calculate: Can you use the perfect square trinomial pattern to factor

  $y^2+16y+64$ .

Answer to Problem 1E

Yes we can use the perfect square trinomial pattern to factories the $y^2+16y+64$ .

The factor of the polynomial is $\left(y+8\right)\left(y+8\right)$ .

Explanation of Solution

Given information: Given polynomial is $y^2+16y+64$ .

Calculation: Given polynomial is $y^2+16y+64$ .

  $\begin{array}{l}=y^2+16y+64\\ =y^2+2\left(y\right)\left(8\right)+{\left(8\right)}^2\\ a^2+2ab+b^2={\left(a+b\right)}^2\\ y^2+2\left(y\right)\left(8\right)+{\left(8\right)}^2={\left(y+8\right)}^2\\ =\left(y+8\right)\left(y+8\right)\end{array}$

Thus, the factor of the polynomial is $\left(y+8\right)\left(y+8\right)$ .