(x+y)^2(x-y)^2

来源：百度知道 编辑：UC知道 时间：2024/05/16 20:27:28
[(x+y)^2][(x-y)^2]
过程.

[x^2+x-5][x^2-x-5]
过程.

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

[x^2+x-5][x^2-x-5]
=(x^2-5)^2-x^2
=x^4-10x^2+25-x^2
=x^4-11x^2+25

(1)(x+y)^2(x-y)^2=[(x+y)(x-y)]^2=[x^2-y^2]^2=x^4-2x^2y^2+y^4
(2)[x^2+x-5][x^2-x-5]=[(x^2-5)+x][(x^2-5)-x]=[(x^2-5)^2-x^2]
=x^4-10x^2+25-x^2=x^4-11x^2+25
{(1)式是用的完全平方公式,(2)是用的平方差公式}

[(x+y)^2][(x-y)^2]
=(X+Y)(X-Y)(X+Y)(X-Y)
=(X^2-Y^2)^2
=X^4+Y^4-2X^2*Y^2

[x^2+x-5][x^2-x-5]
=(X^2-5)^2-X^2
=X^4+25-10X^2-X^2
=X^4-11X^2+25