SOLUTION: How do I factor 25y^2 - 10y + 1? I thought it was a perfect square trinomial, but that doesn't make sense because of the + 1. And I tried factoring it out by taking 5y out, but

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Question 639304: How do I factor 25y^2 - 10y + 1?
I thought it was a perfect square trinomial, but that doesn't make sense because of the + 1. And I tried factoring it out by taking 5y out, but that doesn't match the answer in the back of my book. I don't know how they got that answer. The answer to the question is (5y - 1)^2.
Found 3 solutions by Alan3354, aquyu214, MathTherapy:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website!
How do I factor 25y^2 - 10y + 1?
I thought it was a perfect square trinomial, but that doesn't make sense because of the + 1. And I tried factoring it out by taking 5y out, but that doesn't match the answer in the back of my book. I don't know how they got that answer. The answer to the question is (5y - 1)^2.
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What's wrong with that?
-1*-1 = +1

Answer by aquyu214(10)   (Show Source):
You can put this solution on YOUR website!
(5y)^2-2*(5y)*1+1^2
fit the model that a^2-2ab+b^2=(a-b)^2, that a here is 5y, b here is 1
so that the answer should be (5y-1)^2

Answer by MathTherapy(10553)   (Show Source):
You can put this solution on YOUR website!

How do I factor 25y^2 - 10y + 1?
I thought it was a perfect square trinomial, but that doesn't make sense because of the + 1. And I tried factoring it out by taking 5y out, but that doesn't match the answer in the back of my book. I don't know how they got that answer. The answer to the question is (5y - 1)^2.

We're looking for 2 factors whose product is + 25 (c * a), and whose sum is - 10 (b). These 2 factors are: - 5 and - 5, thus making the replacement for - 10y, - 5y and - 5y.

We now have:

5y(5y - 1) - 1(5y - 1)

(5y - 1)(5y - 1), or

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