If  p + q + r  =  0 , then the value of  2p2(q + r) + 2q2(p + r) + 2r2(p + q)pqr Select an answerA3pqrB 1pqr C6D–6

The given equation is p + q + r = 0.

We are asked to find the value of 2p^2(q + r) + 2q^2(p + r) + 2r^2(p + q) / pqr.

Let's simplify the expression step by step:

Step 1: Substitute p + q + r = 0 in the expression.

We get 2p^2(-p) + 2q^2(-q) + 2r^2(-r) / pqr = -2p^3 - 2q^3 - 2r^3 / pqr.

Step 2: Factor out -2 from the numerator.

We get -2(p^3 + q^3 + r^3) / pqr.

Step 3: Use the identity a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca).

We get -2[(p + q + r)(p^2 + q^2 + r^2 - pq - qr - rp) - 3pqr] / pqr.

Step 4: Substitute p + q + r = 0 in the expression.

We get -2[0 - 3pqr] / pqr = 6pqr / pqr.

Step 5: Cancel out pqr from the numerator and the denominator.

We get 6.

So, the value of the given expression is 6. The correct answer is C6.