因式分解下列各式:(1) xy^2+3xy-10x-y^2+4y-4 (2) (x+2)(x+3)(x-4)(x-5)-44
问题描述:
因式分解下列各式:(1) xy^2+3xy-10x-y^2+4y-4 (2) (x+2)(x+3)(x-4)(x-5)-44
答
(1) xy^2+3xy-10x-y^2+4y-4
= (xy^2+3xy-10x)-(y²-4y+4)
=x(y²+3y-10)-(y-2)²
=x(y+5)(y-2)-(y-2)²
=(y-2)(xy+5x-y+2)
(2) (x+2)(x+3)(x-4)(x-5)-44
=(x+2)(x-4)(x+3)(x-5)-44
=(x²-2x-8)(x²-2x-15)-44
=(x²-2x)²-23(x²-2x)+120-44
=(x²-2x)²-23(x²-2x)+76
=(x²-2x-4)(x²-2x-19)
答
(1) xy^2+3xy-10x-y^2+4y-4=x(y^2+2y-10)-(y^2-4y+4)=x(y+5)(y-2)-(y-2)^2=(xy+5x-y+2)(y-2)(2) (x+2)(x+3)(x-4)(x-5)-44=(x+2)(x-4)(x+3)(x-5)-44=(x^2-2x-8)(x^2-2x-15)-44=(x^2-2x)^2-23(x^2-2x)+120-44=(x^2-2x)...