If $a$ and $b$ are the roots of the equation $x^2-px+q=0$, then find the quadratic equation the roots of which are $(a^2-b^2)(a^3-b^3)$ and $a^3b^2+a^2b^3$.
My Try So I tried to write the roots in the form of sum and products of roots of the given equation. The only doubt that I have is, I can convert every term to the sum and product of roots form ( in terms of $p$ and $q$), but I have no idea how to do the same for the term $(a^2-b^2)$.
If there is another better way to solve this problem, let me know. Thanks for devoting this your time.