解(1) 16a^4-b^4 ^表示乘方

=(4a²)²-(b²)²

=(4a²+b²)(4a²-b²)

=(4a²+b²)(2a+b)(2a-b)

解(2) a²(m-n)+b²(n-m)

=a²(m-n)-b²(m-n)

=(m-n)(a²-b²)

=(m-n)(a+b)(a-b)

解(3) 3(a+1)²-75(a-4)²

=3[(a+1)²-25(a-4)²]

=3﹛(a+1)²-[5(a-4)]²﹜

=3[(a+1)+5(a-4)][(a+1)-5(a-4)]

=3(a+1+5a-20)(a+1-5a+20)

=3(6a-19)(-4a+21)

=-3(6a-19)(4a-21)

解(4) a^(2n+1)-16a^(2n-1)

=[a^(2n-1)]×(a²-16)

=[a^(2n-1)](a+4)(a-4)

解(5) 9(a-b)²-25(a+b)²

=[3(a-b)]²-[5(a+b)]²

=[3(a-b)+5(a+b)][(3(a-b)-5(a+b)]

=(3a-3b+5a+5b)(3a-3b-5a-5b)

=(8a+2b)(-2a-8b)

= -4(4a+b)(a+4b)