p1 = (1 - (1 - p)^3) q^3 // Expand p2 = (1 - (1 - q)^3) p^3 // Expand p1 - p2 // Simplify // Factor Simplify[Sign[p1 - p2], 0 < p < q]
You can solve the inequalities:
Reduce[p1 - p2 > 0 && 0 < p < q, {p, q}] Reduce[p1 - p2 == 0 && 0 < p < q, {p, q}] Reduce[p1 - p2 < 0 && 0 < p < q, {p, q}]
