1.解:a²(b-1)-(b-1)=(b-1)(a²-1)=(b-1)(a+1)(a-1)
2.解:16(x+y)²-25(x-y)²=[4(x+y)]²-[5(x-y)]²=[4(x+y)+5(x-y)]×[4(x+y)-5(x-y)]=(9x-y)(9y-x)
3.解竖唤唯链缺:a²余培(a-b)+b²(b-a)=a²(a-b)-b²(a-b)=(a-b)(a²-b²)=(a-b)²(a+b)
(1)
a²(b-1)-(b-1)
=(a²纯销-1)(b-1)
=(a+1)(a-1)(b-1)
(2)
16(x+y)²-25(x-y)²宽裤吵
=[4(x+y)]²慎侍-[5(x-y)]²
=(4x+4y+5x-5y)(4x+4y-5x+5y)
=(9x-y)(9y-x)
(3)a²(a-b)+b²(b-a)
=(a²-b²)(a-b)
=(a+b)(a-b)(a-b)
=(a+b)(a-b)²