How do you factor 25b^2 - 20by + 4y^2?

1 Answer
Jim H ยท George C.
Sep 18, 2015

25b^2 - 20by + 4y^2 = (5b-2y)^2

Explanation:

25b^2 - 20by + 4y^2

The first term is a perfect square: (5b)^2 = 25b^2

The third term is a perfect square: (2y)^2 = 4y^2

So we MIGHT have (5b +- 2y)^2

We know that (u+-v)^2 = u^2+-2uv+v^2, so we ask ourselves, "Is the middle term (20by) equal to twice the product of the first and second terms of the binomial?"

Yes, it is, so we have:

(5b-2y)^2 = (5b)^2-2(5b)(2y)+ (2y)^2

= 25b^2 - 20by + 4y^2

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