Show that r^2(r + 1)^2 - r^2(r - 1)^2 ≡ 4r^3.

Start with the left hand side (LHS) of the equation. r^2(r + 1)^2 - r^2(r - 1)^2Take the equivalent terms from the separate parts of the LHS outside of set of brackets.r^2[(r + 1)^2 - (r - 1)^2]Expand the interior of the square bracket.r^2[(r^2 + 2r + 1) - (r^2 - 2r + 1)]Simplify the square bracket.r^2[4r]This is equivalent to 4r^3, as desired by the question.