गुणनखण्ड कीजिए : `(ax-by)^(2)+2pq(ax-by)+p^(2)q^(2)`.

Multiply : 5p^(2) + 25pq + 4q^(2) by 2p^(2) - 2pq + 3q^(2)

Add : 6p^(2)q - 5pq^(2) -3pq, 8pq^(2)+2p^(2)q -2pq

Add : 6p^(2)q - 5pq^(2) -3pq, 8pq^(2)+2p^(2)q -2pq

Given that p = -3 and q = 2, evaluate p^(2)+(-pq^(2))-p^(2)q^(2) .

If the abscissa and ordinates of two points P and Q are the roots of the equations x^(2)+2ax-b^(2)=0 and x^(2)+2px-q^(2)=0 respectively,then find the equation of the circle with PQ as diameter.

If the pairs of straight lines ax^(2)+2pxy-ay^(2)=0 and bx^(2)+2qxy-by^(2)=0 be such that each bisects the angles between the other, then (a) p = –q (b) pq = 1 (c) pq = -1 (d) p = q.

Find the excess of 4p^(2)-2pq +3q^(2) over 2p^(2)-pq +4q^(2) .