因式分解(x+2y)(3x^2-4y^2)-(x+2y)^2(x-2y)

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因式分解(x+2y)(3x^2-4y^2)-(x+2y)^2(x-2y)

因式分解(x+2y)(3x^2-4y^2)-(x+2y)^2(x-2y)
因式分解(x+2y)(3x^2-4y^2)-(x+2y)^2(x-2y)

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

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(x+2y)(3x^2-4y^2)-(x+2y)^2(x-2y)
=(x+2y)[(3x^2-4y^2)-(x+2y)(x-2y)] 用平方差公式
=(x+2y)[(3x^2-4y^2)-(x^2-4y^2)]
=(x+2y)(3x^2-4y^2-x^2+4y^2) 同相化简
=2(x+2y)x^2

(x+2y)(3x^2-4y^2)-(x+2y)^2(x-2y)
=(x+2y)〔(3x^2-4y^2)-(2x-4y)〕
=(x+2y))(6x-8y-2x+4y)
=(x+2y)(4x-4y)

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