How to factor 25a^1-(3a+2b)^2?

Question

mertsj · Answer

25a^1  ????

anonymous · Answer

maybe $25a^2$?

anonymous · Answer

whoops yes i meant 25 squared!

anonymous · Answer

so the problem is 25a squared - (3a +2b) squared

anonymous · Answer

$$25a^2-(3a+2b)^2$$ use $x^2-y^2)=(x+y)(x-y)$ with $x=5a,y=(3a+2b)$

anonymous · Answer

That's the difference of two squares: so 

$$a^2-b^2=(a-b)(a+b)  $$

set $$a=\sqrt{25a^1} $$ or $$a=\sqrt{25a^2} $$ whichever one it is. Do the same for the second term, set b to equal the square root of the second term.

anonymous · Answer

YES. my book says factoring when either square is a square of a polynomial

anonymous · Answer

so satellite73, would the answer be (5a+3a+2b)(5a-3a+2b)??

anonymous · Answer

It works whether they are squares or not.

anonymous · Answer

i see, so would that be the answer?? or would you factor both of those trinomials and multiply?

anonymous · Answer

What you have is almost right:

$$ [5a+(3a+2b)]*[5a-(3a+2b))$$
$$ [5a+(3a+2b)]*[5a-3a-2b))$$

check that -2b, you had "+2b" instead.

anonymous · Answer

i see, so when i multiply that, i should get my original question?

anonymous · Answer

Yes.

anonymous · Answer

alright, thank you!