Question

化简(x²+y²)(x²-y²)-(x+y)²(x-y)²

化简求值 x=4 y=1

Answer 1

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

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追问

化简求值 x=4 y=1 最后结果是30么？

追答

代入：
2y²(x-y)(x+y)
=2×1²×(4-1)×(4+1)
=2×1×3×5
=30
结果是30

Answer 2

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

Answer 3

解：原式=x^4-y^4-(x^2+2xy+y^2)(x^2-2xy+y^2)=x^4-y^4-(x^4+y^4-2x^2y^2)=-2y^4+2x^2y^2