9（x+y)²-4（x-y）²分解因式=（5x+y)(5y+x）,我知道这是答案,但是我希望有详细的过程说明.

9（x+y)²-4（x-y）²分解因式=（5x+y)(5y+x）,我知道这是答案,但是我希望有详细的过程说明.
9（x+y)²-4（x-y）²分解因式=（5x+y)(5y+x）,我知道这是答案,但是我希望有详细的过程说明.

9（x+y)²-4（x-y）²分解因式=（5x+y)(5y+x）,我知道这是答案,但是我希望有详细的过程说明.
利用平方差公式
9（x+y)²-4（x-y）²
=[3(x+y)]²-[2(x-y)]²
=[3(x+y)+2(x-y)][3(x+y)-2(x-y)]
=(3x3y+2x-2y)(3x+3y-2x+2y)
=(5x+y)(x+5y)

9（x+y)²-4（x-y）²
=[3(x+y)]^2-[2(x-y)]^2
=[3x+3y]^2-[2x-2y]^2
=(3x+3y+2x-2y)(3x+3y-2x+2y)
=(5x+y)(5y+x)

9（x+y)²-4（x-y）²=[3（x+y）]²-[2(x-y)]²=[3x+3y]²-[2x-2y]²=[(3x+3y)+(2x-2y)]²-[(3x+3y)-(2x-2y)]² =（5x+y)(5y+x).