2(x+y)(x-y)-(x+y)²-(x-y)² 等于多少

2(x+y)(x-y)-(x+y)²-(x-y)² 等于多少
2(x+y)(x-y)-(x+y)²-(x-y)² 等于多少

2(x+y)(x-y)-(x+y)²-(x-y)² 等于多少
2(x+y)(x-y)-(x+y)²-(x-y)²
=-[(x+y)²-2(x+y)(x-y)+(x-y)²]
=-[(x+y)-(x-y)]²
=-(2y)²
=-4y²
运用完全平方公式,要比各项展开再消去简便许多.

=2(x^2-xy+xy-y^2)-(x^2+2xy+y^2)-(x^2-2xy-y^2)
=2x^2-2xy+2xy-2y^2-x^2-2xy-y^2-x^2+2xy+y^2
=-4y^2