Question

Factor Completely:
18a^4-24a^3b+8a^2b^2

The answer is 2a^2(3a-2b)^2, but I have no idea how to solve it.

This is as far as I can get by myself:

18a^4-24a^3b+8a^2b^2
2a^2(9a^2-12ab+4b^2)

I don't know how to continue factoring from there. I'd appreciate any help you could give me. :)

Answer 1

Oh, never mind, I figured it out. To those of you who'd like to know:

18a^4-24a^3b+8a^2b^2
= 2a^2(9a^2-12ab+4b^2)

Factor: 9a^2-12ab+4b^2
Product: 9*4=36 --> -6*-6
Sum: -12 --> -6+(-6)

Bring down 9a^2, both factors, and then 4b^2
= 9a^2-6ab-6ab+4b^2
Factor by grouping:
= (9a^2-6ab)(-6ab+4b^2)
= 3a(3a-2b)-2b(3a-2b)
= (3a-2b)^2

Answer 2

excellent work :)

Answer 3

Thank you! It took me embarrassingly long to solve, though. Lol.

Answer 4

Its kinda like doing FOIL in reverse