Maths F.4!!!

1)When n = 1 ,1 * 5 * 9 is divisible by 3.Assume when n = k the statement is true ,i.e. k(k+4)(k+8) = 3M where M is positive integer.k³ + 12k² + 32k = 3MWhen n = k + 1 :(k+1)(k+5)(k+9)= (k² + 6k + 5)(k + 9)= k³ + 15k² + 59k + 45= (k³ + 12k² + 32k) + 3k² + 27k + 45= 3M + 3(k² + 9k + 15)= 3 (M + k² + 9k + 15) is divisible by 3.By mathematical induction it is true for any positive integer.
2)When n = 1 , 1² (1+1)² = 4 is divisible by 4 ,Assume that the statement is true for n = k , i.e.k² (k+1)² = 4M where M is positive integer.When n = k+1 :(k+1)² (k+2)²= (k + 1)² (k² + 4k + 4)= k² (k+1)² + (4k+4)(k+1)²= 4M + 4(k+1)(k+1)²= 4 [M +(k+1)³] is divisible by 4By mathematical induction it is true for any positive integer.