Factorize:
p3+q3+p+q
Answer:
(p+q)(p2−pq+q2+1)
- We know that (a3+b3)=(a+b)(a2−ab+b2) Thus p3+q3+p+q= (p3+q3)+(p+q)= (p+q)(p2−pq+q2)+(p+q)= (p+q)(p2−pq+q2+1)
- Hence, p3+q3+p+q=(p+q)(p2−pq+q2+1).