因式分解:x^4-2x^3y+4/3x^2y^2-8/27xy^3 在线等!!!!!!!!!!!!!!
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2010-09-22 · 知道合伙人教育行家
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x^4-2x^3y+4/3x^2y^2-8/27xy^3
=x[x^3-2x^2y+4/3xy^2-(2/3y)^3]
=x{[x^3-(2/3y)^3]-2xy(x-2/3y)}
=x[(x-2/3y)(x^2+2/3xy+4/9y^2)-2xy(x-2/3y)]
=x(x-2/3y)(x^2+2/3xy+4/9y^2-2xy)
=x(x-2/3y)(x^2-4/3xy+4/9y^2)
=x(x-2/3y)(x-2/3y)^2
=x(x-2/3y)^3
=x[x^3-2x^2y+4/3xy^2-(2/3y)^3]
=x{[x^3-(2/3y)^3]-2xy(x-2/3y)}
=x[(x-2/3y)(x^2+2/3xy+4/9y^2)-2xy(x-2/3y)]
=x(x-2/3y)(x^2+2/3xy+4/9y^2-2xy)
=x(x-2/3y)(x^2-4/3xy+4/9y^2)
=x(x-2/3y)(x-2/3y)^2
=x(x-2/3y)^3
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