Factoringgg for my Functions & Trig class?

Question

1.) 1 - x2y4

2.) 12x4 - 12

3.) 4x2 - 24x + 36

the numbers right after the variables (x's and y's) are supposed to be powers.

Answer 1

All of these are factorable as the difference of two squares; there are also numeric factors in the last two.  Results:

1. (1 - xy^2)(1 + xy^2)

2. 12(x^4 - 1) = 12 (x^2 + 1)(x^2 - 1) = 12 (x^2 + 1)(x + 1)(x - 1)

3. 4(x^2 -6x + 9) = 4(x - 3)^2.