用因式分解的思想作多项式的除法题[(x^2+y^2)^2-4x^2·y^2]÷(x^2-y^2)

问题描述:

用因式分解的思想作多项式的除法题
[(x^2+y^2)^2-4x^2·y^2]÷(x^2-y^2)

〔(x^2+y^2)^2-4x^2·y^2〕÷(x^2-y^2)
=[(x²+y²+2xy)(x²+y²-2xy)]÷[(x+y)(x-y)]
=[(x+y)²(x-y)²]÷[(x+y)(x-y)]
=(x+y)(x-y)
=x²-y²

〔(x^2+y^2)^2-4x^2·y^2〕÷(x^2-y^2)
〔x^4+y^4-2x^2·y^2〕÷(x^2-y^2)
=(x^2-y^2)^2÷(x^2-y^2)
=(x+y)(x-y)