把25(x+y)²-9(x-y)²因式分解

把25(x+y)²-9(x-y)²因式分解
把25(x+y)²-9(x-y)²因式分解

把25(x+y)²-9(x-y)²因式分解
25(x+y)²-9(x-y)²
=[5(x+y)-3(x-y)][5(x+y)+3(x-y)]
=(2x+8y)(8x+2y)
=4(x+4y)(4x+y)

25(x+y)²-9(x-y)²
=[5(x+y)+3(x-y)][5(x+y)-3(x-y)]
=(8x+2y)(2x+8y)
=4(4x+y)(x+4y)

25(x+y)²-9(x-y)²
=【5（x+y）】²-【3（x-y）】²
=[5(x+y)+3(x-y)][5(x+y)-3(x-y)]
=(8x+2y)(2x+8y)
=2（4x+y）×2（x+4y）
=4(4x+y)(x+4y)

25（x+y)2-9(x-y)2
=25x2+50xy+25y2-9x2+18xy-9y2
=16x2+68xy+16y2
=4(4x2+17xy+4y2)
=4(x+4y)(4x+y)