因式分解:4(x+y)^2-9(x-y)^2

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因式分解:4(x+y)^2-9(x-y)^2
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因式分解:4(x+y)^2-9(x-y)^2
因式分解:4(x+y)^2-9(x-y)^2

因式分解:4(x+y)^2-9(x-y)^2
利用平方差公式:a²-b²=(a+b)(a-b)
4(x+y)²-9(x-y)²
=[2(x+y)]²-[3(x-y)]²
=[2(x+y)+3(x-y)][2(x+y)-3(x-y)]
=(5x-y)(-x+5y)

[2(x+y)+3(x-y)][2(x+y)-3(x-y)]
=(5x-y)(5y-x)

(2x+2y+3x-3y)(2x+2y-3x+3y)=(5x-y)(-x+5y)