Question

Simplify (x2 + 16)(x2 – 16) = ?

A. x4 – 32
B. x4 + 32
C. x4 + 256
D. x4 – 256

Answer 1

You multiply by distributing each term.
(x^2 + 16)(x^2 - 16)
= x^4 - 16x^2 + 16x^2 - 256
= x^4 - 256
So the answer is D

Answer 2

(x² + 16)(x + 8)(x - 2)
(x² + 16)(x(x - 8) + 8(x - 2))
(x² + 16)(x(x) - x(8) + 8(x) - 8(2))
(x² + 16)(x² - 8x + 8x - 16)
(x² + 16)(x² - 16)
x²(x² - 16) + 16(x² - 16)
x²(x²) - x²(16) + 16(x²) - 16(16)
x⁴ - 16x² + 16x² - 256
x⁴ - 256

The answer is D.