question_answer

Factorize: \[{{\mathbf{p}}^{\mathbf{3}}}\mathbf{+}{{\mathbf{q}}^{\mathbf{3}}}\mathbf{+3pq-1}\]

A)  \[(p-q+1)({{p}^{2}}+{{q}^{2}}-pq)\]

B)        \[(p+q-1)({{p}^{2}}+{{q}^{2}}+1-pq+q+p)\]

C) \[{{(p-1)}^{3}}(p+q)\]                                     

D) \[{{(p-1)}^{3}}(p-q)\]

E) None of these