Question

Rút gọn hằng đẳng thức sau

(x²-2x+2)(x²-2)(x²+2x+2)(x²+2)

Answer 1

Ta có: \(\left(x^2-2x+2\right)\left(x^2-2\right)\left(x^2+2x+2\right)\left(x^2+2\right)\)

\(=\left[\left(x^2+2\right)^2-\left(2x\right)^2\right]\left(x^4-4\right)\)

\(=\left(x^4+4x^2+4-4x^2\right)\left(x^4-4\right)\)

\(=\left(x^4+4\right)\left(x^4-4\right)\)

\(=x^8-16\)