Question

How do you find the missing number or term to make a perfect square trinomial $y^2+\frac{1}{2}y+\_?$

Answer 1

Find the missing term of the polynomial:

$y^2+\frac{1}{2}y+\_$

The perfect square trinomial is of the type:

$a^2+2ab+b^2$.

To find the term of the type $b^2$,divide the coefficient of $y$ by $2$ and then squaring the result.

$\begin{array}{rcl}\frac{{\displaystyle \frac{1}{2}}}{2}& =& \frac{1}{2}\times \frac{1}{2}\\ & =& \frac{1}{4}\end{array}$

Squaring the result:

${\left(\frac{1}{4}\right)}^2=\frac{1}{16}$

Also, $y^2+\frac{1}{2}y+\frac{1}{16}={\left(y+\frac{1}{4}\right)}^2$

Hence, the missing term is $\frac{\mathbf{1}}{\mathbf{16}}$.