In ( (a+2b+c)^2 ), what is the sum of the terms containing (bc) and (ac)?

Correct answer: (4bc+2ac)

The direct answer is option B: \(4bc+2ac\). To expand a square containing three terms, use the rule that every pair of different terms produces twice their product. Here the terms are \(a\), \(2b\), and \(c\). For the \(bc\) term, multiply the two terms \(2b\) and \(c\), then double: \(2(2b)(c)=4bc\). For the \(ac\) term, multiply \(a\) and \(c\), then double: \(2(a)(c)=2ac\). Adding these required terms gives \(4bc+2ac\). Option A, \(2bc+2ac\), is wrong because it forgets that the second term is \(2b\), not \(b\). Option B is correct because both pairwise products are calculated with the correct coefficient. Option C, \(2abc\), multiplies three variables, but the question asks for separate two-variable terms, not a three-variable product. Option D, \(4ab+2ac\), contains the \(ab\) pair instead of the requested \(bc\) pair. Memory cue: in a square, each unlike pair gives twice its product; carefully keep the coefficient 2 in \(2b\).