Question

Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared.

$p^2-\frac{1}{3}p$

Short answer

The result is${\left(p-\frac{1}{6}\right)}^2$.

Step-by-step solution

Given Information.  

The Given expression is$p^2-\frac{1}{3}p$.

Identify b, the coefficient of term having power one.  

$p^2-\frac{1}{3}p$

The coefficient of $p$is $-\frac{1}{3}$.

So,$b=-\frac{1}{3}$.

Find 12b2.

Substitute $b=-\frac{1}{3}$.

$$\begin{gathered} ={\left(\frac{1}{2}\times \frac{-1}{3}\right)}^2 \\ ={\left(-\frac{1}{6}\right)}^2 \\ =\frac{1}{36} \end{gathered}$$

Add 136to binomial expression to complete the square.  

$p^2-\frac{1}{3}p+\frac{1}{36}$

Rewrite as a binomial square.

${\left(p-\frac{1}{6}\right)}^2$