Question

Simplify: $(x-y)\left(x^2+y^2\right)\left(x^4+y^4\right)\left(x^8+y^8\right)$.

• A. $x^{16}+y^{16}$
• B. $x^{15}+y^{15}$
• C. $\frac{x^{16}-y^{16}}{x+y}$
• D. $\frac{x^{15}-y^{15}}{x-y}$

Answer 1

Answer: (C)

$(x-y)(x^2+y^2)(x^4+y^4)(x^8+y^8)$
$=\frac{(x+y)(x-y)(x^2+y^2)(x^4+y^4)(x^8+y^8)}{x+y}$
$=\frac{(x^2-y^2)(x^2+y^2)(x^4+y^4)(x^8+y^8)}{x+y}$
$=\frac{(x^4-y^4)(x^4+y^4)(x^8+y^8)}{x+y}$
$=\frac{(x^8-y^8)(x^8+y^8)}{x+y}$
$=\frac{x^{16}-y^{16}}{x+y}$