# How do you factor y^2 + 0.4y + 0.04?

Oct 12, 2017

You can use a process popularly known as completing the square

#### Explanation:

This is how it works: Add and subtract the square of half the coefficient of y to the expression .

The coefficient of y is 0.4. Half of it is $\frac{0.4}{2} = 0.2$

The square of $0.2 = {\left(0.2\right)}^{2}$

Adding and subtracting ${\left(0.2\right)}^{2}$ to the expression ${y}^{2} + 0.4 y + 0.04$ gives ${y}^{2} + 0.4 y + 0.04 + {\left(0.2\right)}^{2} - {\left(0.2\right)}^{2}$

Rearrange that and you get a factorisable expression.

${y}^{2} + {\left(0.2\right)}^{2} + 0.4 y + 0.04 - {\left(0.2\right)}^{2}$

${\left(y + 0.2\right)}^{2} + 0.04 - 0.04$

${\left(y + 0.2\right)}^{2} = \left(y + 0.2\right) \left(y + 0.2\right)$