计算4(x+y)^5(x-y)^4÷[2(x+y)³*(y-x)²]
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计算4(x+y)^5(x-y)^4÷[2(x+y)³*(y-x)²]
4(x+y)^5(x-y)^4÷[2(x+y)³*(y-x)²]
=4(x+y)^5(x-y)^4÷2(x+y)³÷(y-x)²
=4÷2×(x+y)^5÷(x+y)^3×(x-y)^4÷(x-y)^2
=2×(x+y)^(5-3)×(x-y)^(4-2)
=2×(x+y)^2×(x-y)^2
=2[(x+y)(x-y)]^2
=2(x^2-y^2)^2
=2(x^4-2x^2y^2+y^4)
=2x^4-4x^2y^2+2y^4
=4(x+y)^5(x-y)^4÷2(x+y)³÷(y-x)²
=4÷2×(x+y)^5÷(x+y)^3×(x-y)^4÷(x-y)^2
=2×(x+y)^(5-3)×(x-y)^(4-2)
=2×(x+y)^2×(x-y)^2
=2[(x+y)(x-y)]^2
=2(x^2-y^2)^2
=2(x^4-2x^2y^2+y^4)
=2x^4-4x^2y^2+2y^4
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