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

1 Answer
Jim H · 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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