Question

用两种方法计算：（x-y）^2(x+y)^2

Answer 1

（x-y）^2(x+y)^2
=[(x-y)(x+y)]²
=(x²-y²)²
=x^4-2x²y²+y^4

（x-y）^2(x+y)^2
=(x²-2xy+y²)(x²+2xy+y²)
=x^4+2x³y+x²y²-2x³y-4x²y²-2xy³+x²y²+2xy³+y^4
=x^4-2x²y²+y^4

Answer 2

：（x-y）^2(x+y)^2
=[(x-y)(x+y)]²
=（x²-y²）²
=x^4-2x²y²+y^4

（x-y）^2(x+y)^2
=(x²-2xy+y²)(x²+2xy+y²)
=[(x²+y²)-2xy][(x²+y²)+2xy]
=(x²+y²)-4x²y²
=x^4+2x²+y^4-4x²y²
=x^4-2x²y²+y^4

Answer 3

（x-y）^2(x+y)^2
=(x²-y²)²
=x^4-2x²y²+y^4

（x-y）^2(x+y)^2
=(x²+y²-2xy)(x²+y²+2xy)
=(x²+y²)²-4x²y²
=x^4-2x²y²+y^4

Answer 4

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