Question

(x2+1)2-4x(x2-1)因式分解 (x2-x)2+(x2+3x+2)2-4(x2+x+1)2因式分解

Answer 1

(x²+1)²-4x(x²-1)=（x²-1）²-4x(x²-1)+4x²=（x²-1-2x）²

（x^4-2x^3+x²）+（x^4+6x^3+13x²+12x+4）-4（x^4+2x^3+3x²+2x+1）=-2x^4-4x^3+2x²+4x=-2x{x²(x+2)-(x+2)}=-2x(x²-1)(x+2)=-2x(x+1)(x-1)(x+2)