factor the polynomial (p+q)^3-(p-q)^3

Question

factor the polynomial (p+q)^3-(p-q)^3

Answer 1

Using the formula----

(a^3-b^3)=(a-b)(a^2+ab+b^2)

 

(p+q)^3-(p-q)^3=

(p+q-p+q)((p+q)^2+(p+q)(p-q)+(p-q)^2))

 

(2q)(p^2+q^2+2pq+p^2-q^2+p^2+q^2-2pq)

 

(2q)(3p^2+q^2)