Question

Simplify fully
(x^2 +4)^2 - (x^2 - 2)^2

Answer 1

To simplify the expression, we can use the difference of squares formula:

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

We can apply this formula twice to the expression:

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

So, the fully simplified form of the expression is:

4x^2 + 4

Answer 2

12x^2 + 12

Explanation:

1. Remove the parentheses:

x^4 + 8x^2 + 16 - x^4 + 4x^2 - 4

2. Cancel out terms:

8x^2 + 16 + 4x^2 - 4

3. Combine like terms:

12x^2 + 12