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.


{{{25y^2 - 10y + 1}}}


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: {{{25y^2 - 5y - 5y + 1}}}


{{{(25y^2  - 5y) - (5y + 1)}}}


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


(5y - 1)(5y - 1), or {{{highlight_green((5y - 1)^2)}}}


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