f.3 Factorize

k⁴-81
(k²)²-9²
(k²+9)(k²-9)
(k²+9)(k+3)(k-3)

12v-12v²-6u+3u²
12v-6u-12v²+3u²
6(2v-u)-3(4v²-u²)
6(2v-u)-3(2v-u)(2v+u)
(2v-u)(6-6v-3u)
3(2v-u)(2-2v-u)

m⁴ -18m²+81
(m²-9)²
((m+3)(m-3))²

1. k⁴-81
=k⁴-3⁴
=(k²)²-(3²)²
= ( k²-9)(k²+9)
=(k-3)(k+3)(k²+9)

2. 12v-12v²-6u+3u²
=3(4v-4v²-2u+u²)
=3(4v-2u+u²-4v²)
=3(4v-2u+(u+2v)(u-2v))
=6(2v-u)+3(u+2v)(u-2v)
=-6(u-2v)+3(u+2v)(u-2v)
=(u-2v)[-6+3(u+2v)]

3.m⁴ -18m²+81
=(m²)²-2(9)(m²)+9²
=(m²-9)²
=(m+3)²(m-3)²

2009-09-12 11:37:42 補充：
I'm pretty sure my number 2 is right. But cal_cyleung 's number 3 is right and mine's not.