（X+Y)²-16(X-Y）² 如何分解这个因式?

（X+Y)²-16(X-Y）² 如何分解这个因式?
（X+Y)²-16(X-Y）² 如何分解这个因式?

（X+Y)²-16(X-Y）² 如何分解这个因式?
（X+Y)²-16(X-Y）²
=[(X+Y)+4(X-Y)]*[(X+Y)-4(X-Y)]
=(5X-3Y)(5Y-3X)

【参考答案】

(x+y)²-16(x-y)²
=(x+y)²-[4²(x-y)²]
=(x+y)²-(4x-4y)²]
=(x+y+4x-4y)(x+y-4x+4y)
=(5x-3y)(5y-3x)