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To simplify the expression \(2(x+1)(x+2)\), let's first expand it step by step:
1. Expand \((x+1)(x+2)\):
\[
(x+1)(x+2) = x^2 + 2x + x + 2 = x^2 + 3x + 2
\]
2. Now, multiply by 2:
\[
2(x^2 + 3x + 2) = 2x^2 + 6x + 4
\]
So, the expression \(2(x+1)(x+2)\) can be written as:
\[
2x^2 + 6x + 4
\]
Therefore, the correct response is:
**2x² + 6x + 4**.