分解因式用十字相乘(x-y)的平方+3(x的平方-y的平方)-4(x+y)的平方

2025-05-16 14:52:36

推荐回答（4个）

回答1：

(x-y)的平方+3(x的平方-y的平方)-4(x+y)的平方=[(x-y)+4(x+y)][(x-y)-(x+y)]=(5x+3y)(-2y)=-2y(5x+3y)

回答2：

(x-y)^2+3(x^2-y^2)-4(x+y)^2
=x^2-2xy+y^2+3x^2-3y^2-4(x^2+2xy+y^2)
=4x^2-2y^2-2xy-4x^2-8xy-4y^2
=-(6y^2+10xy)

回答3：

(x-y)^2+3(x^2-y^2)-4(x+y)^2
=(x-y)^2+3(x+y)(x-y)-4(x+y)^2
=[(x-y)+4(x+y)][(x-y)-(x+y)]
=-2y(5x+3y)

回答4：

（x-y）^2+3(x-y)(x+y)-4(x+y)^2
=【(x-y)-(x+y)】【x-y+4（x+y）】=-2y(5x+3y)=-10xy-6y^2