In ( (2p+q+r)^2 ), what is the sum of the terms containing (pq) and (pr)?

Correct answer: (4pq+4pr)

The direct answer is B: the sum is \\(4pq+4pr\\). Use the identity \\((a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca\\). Here the three parts are \\(a=2p\\), \\(b=q\\), and \\(c=r\\). The pair containing p and q gives \\(2(2p)(q)=4pq\\). The pair containing p and r gives \\(2(2p)(r)=4pr\\). Therefore their sum is \\(4pq+4pr\\), which may also be written \\(4p(q+r)\\). Option A is wrong because it misses the factor 2 in each cross-product. Option B is correct because both required pair terms have been doubled correctly. Option C is wrong as the coefficient is only half of the required result. Option D is wrong because \\(pqr\\) is a three-variable product, whereas squaring a trinomial produces pairwise cross-products, not a three-variable product. Memory cue: in a square, every pair gets a double product.