Factoring help: (a + b)^2(a - b) - (a + b)(a - b)^2, etc

[sunsetgun]

Hello, I am stuck on three factoring problems:

1) (a+b)^2(a-b) - (a+b)(a-b)^2

I tried using the distributive property to get:

. . .a^2 + b^2 (a-b) - (a+b) a^2 - b^2

Then I simplified it to get:

. . .2ab^2 - 2a^2b

And then I took out the common factors to get:

. . .2ab (b-a)

I am unsure whether that's the correct answer or if I made a mistake using the distributive property.

2) t^3 (2r + s) (3r + 2s) + t^2 (3r + 2s)

I tried using the distributive property to get:

. . .t^3 (6r + 3rs) + (4rs + 2s^2) + t^2 (3r + 2s)

But I'm not sure that I should've even used the distributive property...?

3) (3x + 2y) (x + 2y) + (3x + 2y) (x-2y)

I would like help on where I should start. Simplify by multiplying it out, or use the distributive property, or ...?

Any help would be greatly appreciated! Thanks so much!

 

[stapel]

1) Factor (a + b)²(a - b) - (a + b)(a - b)²

Note that "factoring" just rearranges things; nothing should disappear. Note also that factoring means taking things apart into their factors, not multiplying those factors back together.

Note also that each term has a common factor of (a + b)(a - b):

. . . . .(a + b)[(a + b)(a - b)] - [(a + b)(a - b)](a - b)

Take this out front:

. . . . .[(a + b)(a - b)][(a + b) - (a - b)]

Simplify the stuff in the second set of square brackets.

2) Are the instructions to "factor" on this one?

3) The common factor here is the 3x + 2y.

Eliz.