Simplify the following expression completely.
(x^2 + 16x + 64)(x^2 - 2x - 80)
To simplify the given expression completely, we can use the distributive property to multiply each term in the first set of parentheses by each term in the second set of parentheses.
(x^2 + 16x + 64)(x^2 - 2x - 80)
Simplifying, we get:
= x^2(x^2 - 2x - 80) + 16x(x^2 - 2x - 80) + 64(x^2 - 2x - 80)
= x^4 - 2x^3 - 80x^2 + 16x^3 - 32x^2 - 1280x + 64x^2 - 128x - 5120
Combining like terms, we have:
= x^4 + (16x^3 - 2x^3) - 80x^2 + (64x^2 - 32x^2 + 16x^2) - 1280x - 128x - 5120
= x^4 + 14x^3 + 48x^2 - 1408x - 5120
Therefore, the simplified expression is x^4 + 14x^3 + 48x^2 - 1408x - 5120.