Question

(x-2)(x+2)(x²+2²)(x⁴+2⁴)(x⁸+2⁸)-x¹⁶

Answer 1

\(\left(x-2\right)\left(x+2\right)\left(x^2+2^2\right)\left(x^4+2^4\right)\left(x^8+2^8\right)-x^{16}\)

​\(=\left(x^2-2^2\right)\left(x^2+2^2\right)\left(x^4+2^4\right)\left(x^8+2^8\right)-x^{16}\)

\(=\left(x^4-2^4\right)\left(x^4+2^4\right)\left(x^8+2^8\right)-x^{16}\)

\(=\left(x^8-2^8\right)\left(x^8+2^8\right)-x^{16}\)

\(=\left(x^{16}-2^{16}\right)-x^{16}\)

\(=x^{16}-2^{16}-x^{16}\)

\(\left(-2\right)^{16}=65536\)

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