A level simplify!! please help

Question

Simplify as far as possible:

 

1/6k(k+1)(2k+1)+(k+1)^2

 

The answer should be 1/6(k+1)(k+2)(2k+3) but I keep on getting a different answer. 

Please help, thank you.

Answer 1

1/[6k(k+1)(2k+1)+(k+1)²]=

=(k+1)[k(2k+1)/6+k+1)]=

((k+1)/6)[2k²+k+6k+6]= ((k+1)/6)[2k²+7k+6]=

((k+1)/6)(2k+3)(k+2)=

 1/6(k+1)(k+2)(2k+3)=

 

Note: 2k²+7k+6=2(k+3/2)(k+2)=(2k+3)(k+2)