Find the product `(p-1/p)(p+1/p)(p^2+1/p^2)(p^4+1/p^4)`

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)

Sum the following infinite series (p-q) (p+q) + (1)/(2!) (p-q)(p+q) (p^(2) + q^(2))+(1)/(3!) (p-q) (p+q) (p^(4)+q^(4)+p^(2) q^(2)) + ...oo

Factorize: 27\ p^3-1/(216)-9/2p^2+1/4p

If p is a prime, then sum of log_(p)p^(1//2)-log_(p)p^(1//3)+log_(p)p^(1//4)-……=

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))

Let A, B and C be three mutually exclusive events such that P(A) = p_(1), P(B) = p_(2) " and " P( C) = p_(3) . Then, Let p_(1) = 1/3(1+3p), p_(2) = 1/4(1-p) " and " p_(3) = 1/4(1-2p) , then p belongs to

Let A, B and C be three mutually exclusive events such that P(A) = p_(1) , P(B) = p_(2) and P( C) = p_(3) . Then, Let p_(1) = 1/2(1-p), p_(2) = 1/3(1+2p) " and " p_(3) = 1/5(2+3p) , then p belongs to

If p=-2, find the value of : (i) 4p+7 (ii) -3p^2+4p+7 (iii) -2p^3-3p^2+4p+7