Question

49b^2+70b+25

Answer 1

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Answer 2

Hint: this is a perfect square :)

Answer 3

Hint: 49 is what squared? :P

Answer 4

If you see that the first and last coefficients are perfect squares, then it PROBABLY will be a perfect square trinomial. It can then be factored into:

(px + q)^2 if the second term of the trinomial is positive
(px - q)^2 if the second term of the trinomial is negative

where p is the square root of the 1st coefficient and q is the square root of the last coefficient.

So, in this case:

49b^2 + 70b + 25 ---> [7^2]b^2 + 70b + [5^2]

***note that the second term, 70b is positive

(7b + 5)^2

Now we have to check to make sure it factors out correctly, otherwise, you'll need a new method to factor.

(7b + 5)^2 -----> (7b + 5)(7b + 5)

49b^2 + 35b + 35b + 25

49b^2 + 70b + 25

it works, so (7b + 5)^2 is your answer.

Answer 5

To do this, you can first factor the perfect squares:
(7^2)b^2+70+(5^2)
Factor that again, and you get
(7b+5)^2 or it can be written as (7b+5)(7b+5)
That is your answer when factored.