{(xy+2)(xy-2)-2(x²y²-2)}÷(xy)=?

{(xy+2)(xy-2)-2(x²y²-2)}÷(xy)=?
{(xy+2)(xy-2)-2(x²y²-2)}÷(xy)=?

{(xy+2)(xy-2)-2(x²y²-2)}÷(xy)=?

原式=[(x²y²-4)-2x²y²+4]÷(xy)
=(-x²y²)÷(xy)
=-xy

首先观察可得(xy+2)(xy-2)为完全平方，相乘后得x²y²-4
则此时{(xy+2)(xy-2)-2(x²y²-2)}÷(xy)化简为{(x²y²-4-2(x²y²-2)}÷(xy)
继续化简可得：{(x²y²-4-2x²y²+4}÷(xy)=-x²...

全部展开

首先观察可得(xy+2)(xy-2)为完全平方，相乘后得x²y²-4
则此时{(xy+2)(xy-2)-2(x²y²-2)}÷(xy)化简为{(x²y²-4-2(x²y²-2)}÷(xy)
继续化简可得：{(x²y²-4-2x²y²+4}÷(xy)=-x²y²/（XY）=-XY
即{(xy+2)(xy-2)-2(x²y²-2)}÷(xy)=-XY

收起