Chapter 7.1, Problem 18OE

To determine

To Find:

What must be added to make the expression a trinomial square:

  $y^2+\frac{2}{5}y+?$

Answer to Problem 18OE

  $\frac{1}{25}$

Explanation of Solution

Given:

The expression is :

  $y^2+\frac{2}{5}y+?$

Calculation:

Given:

  $y^2+\frac{2}{5}y+?$

First , make the coefficient of $y^2$ 1.

Since here , it already is 1.

Check for the coefficient of y .

It is $\frac{2}{5}$ .

So, the term that has to be added to make it a trinomial and a perfect square is :

square of the half of the coefficient of y

  $={\left(\frac{2}{5}\cdot \frac{1}{2}\right)}^2=\frac{1}{25}$

So, $\frac{1}{25}$ should be added.

Check:

  $y^2+\frac{2}{5}y+\frac{1}{25}={\left(y+\frac{1}{5}\right)}^2$