algebra help plz..?

Question

factor

show me how 2 do dis prob. step by step..plz i wanna learn

1. 5x^3y^3-10x^2y^3+5xy^3


2. 27xyz^2 -12xy

Answer 1

Mainly, you look for common terms. You can separately handle constants, powers of x, powers of y, and powers of z.

So in the first one there are common factors of 5, x, and y^3. Pulling them out, you have 5xy^3 * (x^3 - 2x^2 + 1).

It so happens that x^3 - 2x^2 + 1 equals zero when x=1. Hence, it is divisible by x-1. In particular, it equals (x-1)*(x^2-x-1). x^2-x-1 is indeed irreducible, as you could check by solving it via the quadratic formula and getting messy answers, so that tells you what a complete factorization of the original polynomial is.

For Number 2, pull out the common factors 3, x, and y. That gives you 3xy(9z^2-4). Well, you're supposed to recognize that 9z^2-4 is the difference between two squares, namely of 3z and 2, and hence equals (3z+2)(3z-2).

That's how to do it. :)