x+y的和乘以x+y+2xy的积加上x平方y平方减去一怎么因式分解?
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(X+Y)(X+Y+2XY)+X²Y²-1
=X²+XY+2X²Y+Y²+XY+2XY²+X²Y²-1
=X²+2XY+Y²+2X²Y+2XY²+X²Y²-1
=(X+Y)²+2XY(X+Y)+X²Y²-1
=(X+Y+XY)²-1
=(X+Y+XY+1)(X+Y+XY-1)
=X²+XY+2X²Y+Y²+XY+2XY²+X²Y²-1
=X²+2XY+Y²+2X²Y+2XY²+X²Y²-1
=(X+Y)²+2XY(X+Y)+X²Y²-1
=(X+Y+XY)²-1
=(X+Y+XY+1)(X+Y+XY-1)
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