Question

Solve the following:
$(x^4-y^4)(x^4+y^4)(x^8-y^8)(x^{16}-y^{16})$

Answer 1

$\begin{array}{c}\left(x^4-y^4\right)\left(x^4+y^4\right)\left(x^8-y^8\right)\left(x^{16}-y^{16}\right)\\ \Rightarrow \left(x^8-y^8\right)\left(x^8+y^8\right)\left(x^{16}-y^{16}\right)\left[a^2-b^2=\left(a-b\right)\left(a+b\right)\right]\\ \Rightarrow \left(x^{16}-y^{16}\right)\left(x^{16}+y^{16}\right)\\ \Rightarrow {\left(x^{32}-y^{32}\right)}^{}Ans.\end{array}$