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

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Answer 1 · 2017-10-12T09:24:29

You can use a process popularly known as completing the square

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 $0.4/2 = 0.2$

The square of $0.2 = (0.2)^2$

Adding and subtracting $(0.2)^2$ to the expression $y^2+0.4y+0.04$ gives $y^2+0.4y+0.04 + (0.2)^2 - (0.2)^2$

Rearrange that and you get a factorisable expression.

$y^2 + (0.2)^2 + 0.4y + 0.04 - (0.2)^2$

$(y + 0.2)^2 + 0.04 - 0.04$

$(y + 0.2)^2 = (y + 0.2)(y + 0.2)$

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