How do you factor y^2 + 0.4y + 0.04y2+0.4y+0.04?

1 Answer
Samuel A.
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 0.4/2 = 0.2 0.42=0.2

The square of 0.2 = (0.2)^20.2=(0.2)2

Adding and subtracting (0.2)^2(0.2)2 to the expression y^2+0.4y+0.04y2+0.4y+0.04 gives y^2+0.4y+0.04 + (0.2)^2 - (0.2)^2y2+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)^2y2+(0.2)2+0.4y+0.04−(0.2)2

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

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

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