Sums and differences of cubes help?

Question

Factor completly



1) 2y^3 -128

2) 2y^3 - 54z^3

Answer 1

Hi,
Well, the formula for the difference of two cubes in this:
(a^3 -b^3) = (a-b)(a² +ab +b²)
So, let's dee how yur problem fits into that formula:
Prob 1)
2y^3 -128
2(y^3 -64) (ALWAYS take out greatest common factor.)
Now, take the cube root of both terms inside the parentheses.
(y-4)
Now, write the second part according to the formula, or you can do this: Square the first term of the binomial, multiply the two terms and put a plus sign before it, square the last term of the binomial. Remember that sign of the middle term of the trinomial is always opposite to the sign inside the binomial
2(y-4)(y^2 +4y+16) (Don't forget the GCF.)

Prob 2)
2y^3 - 54z^3
2(y^3-27z^3) (Same routine with GCF)
2(y-3z)(y^2 +3yz +9z² )

Hope this helps.
FE