Math problems...help?

Question

Factor each one completely.

I am stuck, i dont know how to solve these two

!

1. x^2 - yz + xz - xy

2. a^3 - 2b^2 + 2a^2 b - ab

thanks so much

!

Answer 1

1. x^2 - yz + xz - xy = z(x - y) + x(x - y) = (z + x)(x - y)

2. a^3 - 2b^2 + 2a^2 b - ab = a^3 + 2a^2b - (ab + 2b^2)

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

The trick on both of these is to regroup the terms and find a common term.  On the first one it was (x - y).  On the second, it was (a + 2b).

Answer 2

1. x^2 - yz + xz - xy

x^2 - xy - yz + xz

x(x - y) - z(x- y)

(x - y)(x - z)

2. a^3 - 2b^2 + 2a^2b - ab

a^3 + 2a^2b - 2b^2 - ab

a^3 - ab + 2a^2b - 2b^2

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