Question

How do you solve(3x+1)²- (x-2)²
factorization a²b+ab+ab²-a-b-1

Answer 1

I believe the answer is $8x^{2}+2x+5$

First thing's first:  Square both of the parentheses, I'm going to use the FOIL method, if you use a different method, go for it:

$(9x^{2}+6x+1)-(x^{2}-4x+4)$

Now distribute the $-$ to the second parentheses to make it a plus sign:

$9x^{2}+6x+1-x^{2}+4x-4$

Now combine like factors to simplify:

$8x^{2}+10x-3$

So that should be your final answer if I understand the question correctly.

Answer 2

All you do is FOIL the (3x+1)^2 and then FOIL the (x-2)^2. The only challenge here is that you have to multiply all the terms in the (x-2)^2 FOIL by -1 because its -(x-2)^2. Once you get all the terms from FOIL just simplify by combining like terms.