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x3-y3和x3+y3怎么因式分解

来源:学生作业帮 编辑:作业帮 分类:综合作业 时间:2024/06/02 16:56:18
x3-y3和x3+y3怎么因式分解
X³-Y³=X³-XY²+XY²-Y³
=X(X²-Y²)+Y²(X-Y)
=X(X-Y)(X+Y)+Y²(X-Y)
=(X-Y)[X(X+Y)+Y²]
=(X-Y)(X²+XY+Y²)
X³+Y³=X³+X²Y-X²Y+Y³
= X²(X+Y)-Y(X²-Y²)
=X²(X+Y)-Y(X-Y)(X+Y)
=(X+Y)[X²-Y(X-Y)]
=(X+Y)(X²-XY+Y²)