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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)

因式分解