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To rewrite the expression \(2(x+1)(x+2)\), we first need to expand it.
1. Start by expanding the binomials:
\[
(x + 1)(x + 2) = x^2 + 2x + 1x + 2 = x^2 + 3x + 2
\]
2. Now, multiply this result by 2:
\[
2(x^2 + 3x + 2) = 2x^2 + 6x + 4
\]
So, the expanded form of the expression \(2(x + 1)(x + 2)\) is \(2x^2 + 6x + 4\).
Therefore, the correct answer is:
**C) 2x^2 + 6x + 4**.