Разложите многочлен на множители:

1) (а-12) ^3 - 125

2) (b+4) ^3+64

3) 81 - (с^2+6 с) ^2

4) 16m^2 - (m-n) ^2

1) (а-12) ³ - 125 = (a-12) ³-5³ = (a-12-5) ((a-12) ² + (a-12) * 5+5²) =

= (a-17) (a²-24a+144+5a-60+25) =

= (a-17) (a²-19a+109)

2) (b+4) ³+64 = (b+4) ³+4³ = (b+3+4) ((b+3) ² + (b+3) * 4+4²) =

= (b+7) (b²+6b+9+4b+12+16) =

= (b+7) (b²+10b+37)

3) 81 - (с²+6 с) ²=9² - (c²+6c) ² = (9+c²+6c) (9-c²-6c) = (c+3) ² (9-c²-6c)

4) 16m ² - (m-n) ² = (4m) ² - (m-n) ² = (4m+m-n) (4m-m+n) = (5m-n) (3m+n)