Question

Show that (9p+5q)square +180pq = (9p-5q)square

Answer 1

Your question has a small mistake. it should be -180pq.

$LHS= (9p+5q)^{2} - 180pq \\ \\ = {(9p)}^{2} + {(5q)}^{2} + 2 \times 9p \times 5q - 180pq \\ \\ = 81 {p}^{2} + 25 {q}^{2} + 90pq - 180pq \\ \\ = 81 {p}^{2} + 25 {q}^{2} - 90pq \\ \\ = {(9p)}^{2} + {(5q)}^{2} - 2 \times 9p \times 5q \\ \\ = {(9p - 5q)}^{2} \\ \\ = RHS$