81(x+2y)^2-9(x-3y)^2 因式分解

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81(x+2y)^2-9(x-3y)^2 因式分解

81(x+2y)^2-9(x-3y)^2 因式分解
81(x+2y)^2-9(x-3y)^2 因式分解

81(x+2y)^2-9(x-3y)^2 因式分解
81(x+2y)^2-9(x-3y)^2
=[9(x+2y)]^2-[3(x-3y)]^2————积的乘方
=[9(x+2y)+3(x-3y)][9(x+2y)-3(x-3y)]————平方差公式
=(9x+18y+3x-9y)(9x+18y-3x+9y)————去括号
=(12x+9y)(6x+27y)————合并同类项
=3(4x+3y)*3(2x+9y)————提公因式
=9(4x+3y)(2x+9y)————小学学的,不用我说了.

81(x+2y)^2-9(x-3y)^2
=[9(x+2y)]^2-[3(x-3y)]^2
=[9(x+2y)-3(x-3y)][9(x+2y)+3(x-3y)]
=(6x+27y)(12x+9y)
=9(2x+9y)(4x+3y).

81(x+2y)^2-9(x-3y)^2 因式分解
=[9(x+2y)+3(x-3y)][9(x+2y)-3(x-3y)]
=9*(4x-3y)(2x+9y)

81(x+2y)^2-9(x-3y)^2
=9[9(x+2y)^2-(x-3y)^2]
=9[(3x+6y)^2-(x-3y)^2]
=9(3x+6y+x-3y)(3x+6y-x+3y)
=9(4x+3y)(2x+9y)

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