Question

分解因式,要详细过程

X^6-Y^6
x^4-2x^3-35x^2

Answer 1

X^6-Y^6
=(x^3)^2-(y^3)^2
=(x^3+y^3)(x^3-y^3) 利用立方和，立方差公式
=(x+y)(x^2-xy+y^2)(x-y)(x^2+xy+y^2)
=(x^2-y^2)(x^2+y^2-xy)(x^2+y^2+xy)
=(x^2-y^2)[(x^2+y^2)^2-(xy)^2]

x^4-2x^3-35x^2
=x^2(x^2-2x-35)
=x^2(x-7)(x+5)

Answer 2

X^6-Y^6
=(x³)²-(y³)²
=(x³+y³)(x³-y³)
=(x+y)(x²-xy+y²)(x-y)(x²+xy+y²)

x^4-2x^3-35x^2
=x²(x²-2x+1-36)
=x²[(x-1)²-6²]
=x²(x-1+6)(x-1-6)
=x²(x+5)(x-7)