分解因式 4m^2(x+y)^2-12mn(x+y)(x-y)+9n^2(x-y)^2?

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分解因式 4m^2(x+y)^2-12mn(x+y)(x-y)+9n^2(x-y)^2?

分解因式 4m^2(x+y)^2-12mn(x+y)(x-y)+9n^2(x-y)^2?
分解因式 4m^2(x+y)^2-12mn(x+y)(x-y)+9n^2(x-y)^2?

分解因式 4m^2(x+y)^2-12mn(x+y)(x-y)+9n^2(x-y)^2?
4m^2(x+y)^2-12mn(x+y)(x-y)+9n^2(x-y)^2
=[2m(x+y)]²-2×2×3mn(x+y)(x-y)+[3n(x-y)]²
=[2m(x+y)-3n(x-y)]²
=(2mx+2my-3nx+3ny)²

完全平方
原式=[2m(x+y)-3n(x-y)]²
=(2mx+2my-3nx+3ny)²