In ( (a+3b+c)^2 ), where does (6ab) come from?

Correct answer: From (2\times a\times3b)

The direct answer is B: the term 6ab comes from the pair product 2 × a × 3b. For three terms, use the identity \\(p+q+r\\)^2=p^2+q^2+r^2+2pq+2qr+2rp\\). Here the three terms are a, 3b, and c. The pair a and 3b produces 2(a)(3b)=6ab. Thus the required mixed term is formed by doubling the product of those two terms. Option A, a², is only the square of the first term and has no b. Option B is correct because 2 × a × 3b simplifies to 6ab. Option C gives 2(3b)c=6bc, not 6ab, because it uses the second and third terms. Option D gives (3b)²=9b², which is a square term, not the mixed term involving a and b. The same expansion also contains a², 9b², c², 6ab, 6bc, and 2ac. Memory cue: in a square of several terms, every pair contributes twice its product. Decision: pass; the algebra and supplied option B are correct.