Show that `(9p-5q)^2+180pq=(9p+5q)^2

Show that (4pq+3q)^2-(4pq-3q)^2 = 48pq^2

The p^(th), q^(th) and r^(th) terms of an A.P. are a, b, c, respectively. Show that (q-r) a+(r-p) b+(q-p)c = 0

If p, q, are real and p ne q then the roots of the equation (p-q) x^(2)+5(p+q) x-2(p-q)=0 are

Show that |(x,p,q),(p,x,x),(q,q,x)| = (x - p)(x^(2) + px - 2q^2)

If p^(th), q^(th), r^(th) and s^(th) terms of an A.P. are in G.P, then show that (p – q), (q – r), (r – s) are also in G.P.

Show that the points P(- 2 , 3, 5) , Q (1, 2, 3) and R(7, 0, -1) are collinear.

Prove that |(x,p,q),(p,x,q),(p,q,x)| = (x - p)(x - q)(x + p +q)

Simplify (2.5 p-1.5 q)^2-(1.5 p-2.5 q)^2

Subtract: 4pq-5q^2-3p^2 from 5p^2+3q^2-pq