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To rewrite the expression \( 2(x+1)(x+2) \), we can first expand the factors and then multiply by 2.
1. First, expand \( (x+1)(x+2) \):
\[
(x+1)(x+2) = x^2 + 2x + x + 2 = x^2 + 3x + 2
\]
2. Now, multiply this result by 2:
\[
2(x^2 + 3x + 2) = 2x^2 + 6x + 4
\]
Thus, the expression \( 2(x+1)(x+2) \) can be rewritten as \( 2x^2 + 6x + 4 \).
So, the correct response is:
**2x^2 + 6x + 4**