Question

http://www.sketchtoy.com/38665436

@johnweldon1993

Answer 1

@zairhenrique if you want to jump in go right ahead I'm working it out lol

Answer 2

What's the question rs? Factoring ?

Answer 3

Factoring, yes.

Answer 4

I mean I know the answer but how to explain it is annoying lol...so please...and yes factoringg

Answer 5

I got that.

Answer 6

Okay well basically....you have 2 variables...'a' and 'b'

(a b) (a b)

what 2 numbers add to get 12 and multiply to get 27

Answer 7

9 and 3?

Answer 8

\[a²+12ab+27b² = a²+12ab +36b² - 9b²\]\[a²+12ab+36b²-9b²=(a+6b)²-9b²\]\[(a+6b)²-9b²=(a+6b+3b)(a+6b-3b)=(a+9b)(a+3b)\]

Answer 9

Perfect...so use 9 and use 3 for your coefficients of 'b'

(a + 9b)(a + 3b)

I wish I could explain it more... lol

Answer 10

That's it:?

Answer 11

Yep.

Answer 12

That would be it lol

Answer 13

Just a trick, if you don't how to factor something like that, just try to solve it for one variable, just for example, solving it for a.

\[a²+12b*a +27b²\]
\[a=\frac{ -12b \pm \sqrt{(12b)²-4*27b²} }{ 2 }=\frac{ -12b \pm \sqrt{144b²-108b²} }{ 2 }\]\[a=\frac{ -12b \pm \sqrt{36b²} }{ 2 }=\frac{ -12b \pm 6b }{ 2 }=-6b \pm3b\]
\[a=-6b+3b=-3b \iff a=-6b-3b=-9b\]
So, if the roots are -3b and -9b, the equation is:\[(a-(-3b)(a-(-9b)=(a+3b)(a+9b)\]It's a hard and long way to do that, but, it's a way when you are in troubles haha