Question

In the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared.

$m^2-8m$

Short answer

The required binomial square is${\left(m-4\right)}^2$.

Step-by-step solution

Step 1. Given information.

The given quadratic equation is:

$m^2-8m$

Step 2. Complete the square.

$m^2-8m$

The coefficient of mis 8.

Now find ${\left(\frac{1}{2}b\right)}^2$,

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

Now add 16 to the binomial to complete the square,

$m^2-8m+16$

Rewrite as a binomial square,

${\left(m-4\right)}^2$