Let's simplify using formula.
`(3p+2q-4r)^2 + 2(3p+2q-4r)(4r-2p-q) + (4r-2p -q)^2`

Using formula let's show that. (2p-q)^2 = (2p+q)^2 - 8pq

Simplify the following: (6p-4q+2r) + (2p+3q-4r)

Let's express the following in the product from using formula. (m+p+q)^2 - (m-p-q)^2

Let's resolve into factors: (p^2 - 3q^2)^2 - 16 (p^2 - 3q^2) + 63

If the pth, qth, and rth terms of an A.P. are in G.P., then the common ratio of the G.P. is a. (p r)/(q^2) b. r/p c. (q+r)/(p+q) d. (q-r)/(p-q)

Let's prove (p+q)^4 - (p-q)^4 = 8pq(p^2 + q^2)

Let alpha,beta be the roots of the equation x^(2)-px+r=0 and alpha//2,2beta be the roots of the equation x^(2)-qx+r=0 , then the value of r is (1) (2)/(9)(p-q)(2q-p) (2) (2)/(9)(q-p)(2p-q) (3) (2)/(9)(q-2p)(2q-p) (4) (2)/(9)(2p-q)(2q-p)

Let 's subtract. (2q^2 + 3p^2 - qp + pq^2) From (p^2 + q^2 - pq + p^2q) .

Tangent is drawn at any point (p ,q) on the parabola y^2=4a xdot Tangents are drawn from any point on this tangant to the circle x^2+y^2=a^2 , such that the chords of contact pass through a fixed point (r , s) . Then p ,q ,r and s can hold the relation (a) r^2q=4p^2s (b) r q^2=4p s^2 (c) r q^2=-4p s^2 (d) r^2q=-4p^2s

Simply (a^(p)/a^(q))^(p+q-r).(a^(q)/a^(r ))^(q+r-p).(a^(r )/a^(p))^(r+p-q)