Question

Rút gọn: (x+1)^4-6(x+1)^2-(x^2-2)(x^2+2)

Answer 1

(x + 1)^4 - 6(x + 1)^2 - (x^2 - 2)(x^2 + 2)

= (x^2 + 2x + 1)(x^2 + 2x + 1) - 6(x^2 + 2x + 1) - (x^2 - 2)(x^2 + 2)

= x^2.(x^2 + 2x + 1) + 2x.(x^2 + 2x + 1) + x^2 + 2x + 1 - (x^2 - 2)(x^2 + 2)

= x^4 + 2x^3 + x^2 + 2x^3 + 4x^2 + 2x + x^2 + 2x + 1 - 6x^2 - 12x - 6 - x^2 + 2^2

= 4x^3 - 8x - 1

Answer 2

\(\left(x+1\right)^4-6\left(x+1\right)^2-\left(x^2-2\right)\left(x^2+2\right)\)

\(=\left(x^2+2x-5\right)\left(x^2+2x+1\right)-x^4+2\)

\(=x^4+2x^3+x^2+2x^3+4x^2+2x-5x^2-10x-5-x^4+4\)

\(=4x^3-8x-1\)

Answer 3

Bro ok