已知x-y=1,求代数式x的四次方-xy的三次方-x的三次方y-3x的平方y+3xy的平方+y的四次方

2025-05-20 00:43:06
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回答1:

x^4-XY^3-X^3Y-3X²Y+3XY²+Y^4
=X^3(X-Y)-Y^3(X-Y)-3XY(X-Y)
=X^3-Y^3-3XY
=(X-Y)(X²+XY+Y²)-3XY
=X²+XY+Y²-3XY
=X²-2XY+Y²
=(X-Y)²
=1