Question

Factor the expression 3x^2y^2 - 6x^2 - 12y^2 - 24 completely.

A) a(3x^2 + 4)(y^2 + 2)
B) 3(x^2 + 4)(y^2 + 2)
C) 3(x^2y^2 - 2x^2)(4y^2 + 8)
D) (x^2 + 4)(y^2 + 2)

Answer 1

To factor the expression 3x^2y^2 - 6x^2 - 12y^2 - 24 completely, you can group the terms and factor out common terms from each grouping.

Step-by-step explanation:

To factor the expression 3x^2y^2 - 6x^2 - 12y^2 - 24 completely, we can first group the terms:

(3x^2y^2 - 6x^2) - (12y^2 + 24)

Now, we can factor out common terms from each grouping:

3x^2(y^2 - 2) - 12(y^2 + 2)

This simplifies to:

(3x^2 - 12)(y^2 - 2)

So, the completely factored expression is (3x^2 - 12)(y^2 - 2).