Factoring:9a^2+6ab+1b^2-25
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Factoring:9a^2+6ab+1b^2-25

[From: ] [author: ] [Date: 12-07-04] [Hit: ]
Except, instead of x you have 3a + b.(3a + b)^2 - 25 = (3a + b - 5)(3a + b + 5) and that is completely factored.-The first three terms form a perfect square trinomial. Factor this, then factor as the difference of two squares.......
I have no clue as to where to even start. I appreciate any help Thank you in advance.

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If you look at the first three terms, you can factor those

9a^2 + 6ab + b^2 (this is a perfect square trinomial)
(3a + b) (3a +b)
(3a + b)^2

Put it back into what you had

(3a + b)^2 - 25.

Now, notice if you had x^2 - 25, you can factor that into (x - 5)(x + 5) since it is a difference of squares. Well, that is what you have. Except, instead of x you have 3a + b. So you just replace x in

x^2 - 25 = (x - 5)(x + 5)

with 3a + b to get

(3a + b)^2 - 25 = (3a + b - 5)(3a + b + 5) and that is completely factored.

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The first three terms form a perfect square trinomial. Factor this, then factor as the difference of two squares.

(3a + b)² - 25 = (3a + b + 5)(3a + b - 5)

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(-5+3a+b) (5+3a+b)
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