a^2-12ab+36b^2 factor the trinomial, no clue, need some help please..

Question

kamille · Answer

have you ever heard of formula

$$(a-b)^{2}=a ^{2}-2ab+b ^{2}$$

anonymous · Answer

no, I haven't :/

kamille · Answer

Oh :/ so, look at my given formula, can you see any similiarity with my formula and your problem?

anonymous · Answer

yeah, I see it what do i do, do i find what multiplies to 36 and adds upto 12?

kamille · Answer

nah, not multiplies to 36. if you have b^2 then if you want to get b, you need to $$\sqrt{b ^{2}}$$ and you get an answer b. So if you have 36 then you need $$\sqrt{36}$$ what do you get?

anonymous · Answer

6?

kamille · Answer

yes, you are right so you have a=a (because in your problem there is no number by a, right, and you get b=6. So, according to the formula, what do you get?

anonymous · Answer

im so sorry it was 35b^2

anonymous · Answer

not 36

anonymous · Answer

so i just did it X+7y and x+5y

anonymous · Answer

Well, you have two equations for each of the things. The 12 is negative so you need the two numbers to add up to negative 12

$$(a + xb)(a + yb) = a^2 + (x+y)ab + xyb^2$$

if you want two numbers x and y that add up to -12 and multiply to 35, then

x + y = -12
xy = 35

You can solve for x or y in one equation and substitute into the other.

anonymous · Answer

i think i got it, thank you both!!