Question

Factor:
36b^2 +60bf +25f^2 = (? ?) (? ?)

Answer 1

wow ok find factors of 36*25 that add up to 60

Answer 2

right, and I feel like I gone through every possible combo and nothing is adding up to 60?!

Answer 3

25f^2+60bf+36b^2=(5f+6b)(5f+6b)
Do you want to know how i got the answer?

Answer 4

for sure please!

Answer 5

how the he*& did I miss that one??? ugh. you are fast...

Answer 6

Well what I did first was rearrange the equation so that f^2 was our leading term
from there I used a technique to find my terms
in order to get 25f^2 I would have to multiply 5f by 5f

Answer 7

oh because the first and last coefficient are perfect squares...
it comes out to be a perfect square...

Answer 8

Now some would figure how to get the second term, but that would actually be a much more tedious process so I moved to 36b^2
So...in order to get 36b^2, i would have to multiply 6b by 6b
Now all I have to do combine my terms into binomials to get (5f+6b)
And since we are multiplying 5f by 5f and 6b by 6b to get our first and last term, I came up with the binomials
(5f+6b)(5f+6b)
And if you notice, the product ends up to be...
(5f+6b)(5f+6b)=25f^2+30bf+30bf+36b^2
=25f^2+60bf+36b^2

Answer 9

and you knew to use the factors you used rather than other factors because the terms are squared? or what made you so sure not to use 12*3 for 36, for example?

Answer 10

how did you avoid the trial and error method is what I am wondering?

Answer 11

Yeah, I basically found my terms because they were perfect squares. If they weren't I wouldve found them with a different method.