Question

Complete the square to make a perfect square trinomial. Write the result as a binomial square.

$z^2+8z$

Short answer

The result is$(z+4{)}^2$.

Step-by-step solution

Given Information.  

The Given expression is$z^2+8z$.

Identify b the coefficient of term having power one.   

$z^2+8z$

The coefficient of $z$is $8$.

So,$b=8$

Find 12b2.

Substitute $b=8$

$$\begin{gathered} ={\left(\frac{1}{2}\times 8\right)}^2 \\ ={\left(4\right)}^2 \\ =16 \end{gathered}$$

Add 16 to binomial expression to complete the square.   

$z^2+8z+16$

Rewrite as a binomial square.

$(z+4{)}^2$