Question 165860
Factor:
{{{(p+q)^3-(p-q)^3}}} This is a "difference of cubes" and can be factored thus:
{{{A^3-B^3 = (A-B)(A^2+AB+B^2)}}} where: A = (p+q) and B = (p-q), so...
{{{(p+q)^3-(p-q)^3 = ((p+q)-(p-q))((p+q)^2+(p+q)(p-q)+(p-q)^2)}}} Simplifying this we get:
{{{(p+q)^3-(p-q)^3 = (p+q-p+q)((p^2+2pq+q^2)+(p^2-q^2)+(p^2-2pq+q^2))}}} Combining like-terms, we get:
{{{(p+q)^3-(p-q)^3 = highlight(2q(3p^2+q^2))}}}