Question

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

$a^2+10a$

Short answer

The result is$(a+5{)}^2$.

Step-by-step solution

Given Information.

The Given expression is$a^2+10a$.

Identify b, the coefficient of term having power one.

$a^2+10a$

The coefficient of $a$is $10$.

Therefore,$b=10$.

Find 12b2.

Since $b=10$

$={\left(\frac{1}{2}\times 10\right)}^2$

$={\left(5\right)}^2=25$

Add 12b2to binomial expression to complete the square.

Since ${\left(\frac{1}{2}b\right)}^2=25$

Therefore, $a^2+10a+25$

Rewrite as a binomial square.

$(a+5{)}^2$.