Find each of the products: `(4/3p q^2)xx(-1/4p^2r)xx\ (16 p^2q^2r^2)`

Find the products: (7p^4+q)(49 p^8-7p^4q+q^2)

Find the value of : 1/2 p^(2) xx 4p^(2)q xx(-3 p)

Factorize each of the following expressions: (1) q r-p r+q s-p s (2) p^2q-p r^2-p q+r^2 (3) 1+x+x y+x^2y (4) a x+a y-b x-b y

If the roots of the equation 1/ (x+p) + 1/ (x+q) = 1/r are equal in magnitude but opposite in sign, show that p+q = 2r & that the product of roots is equal to (-1/2)(p^2+q^2) .

Factorise : (p^(2) + q^(2) - r^(2))^(2) - 4p^(2)q^(2) .

If each pair of the three equations x^(2) - p_(1)x + q_(1) =0, x^(2) -p_(2)c + q_(2)=0, x^(2)-p_(3)x + q_(3)=0 have common root, prove that, p_(1)^(2)+ p_(2)^(2) + p_(3)^(2) + 4(q_(1)+q_(2)+q_(3)) =2(p_(2)p_(3) + p_(3)p_(1) + p_(1)p_(2))

Express each of the rational number of the form p/q : (3/8)^(-2)xx\ (4/5)^(-3)

Tangent is drawn at any point (p ,q) on the parabola y^2=4a x .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

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

Factorize each of the following algebraic expressions: 4x^2+12 x y+9y^2 (2) 9a^2-24 a b+16 b^2 (3) p^2q^2-6p q r+9r^2 (4) 36 a^2+36 a+9