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)#