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To rewrite the expression \( 2(x + 1)(x + 2) \), we first expand the product inside the parentheses and then distribute.
1. Start with the inner expression:
\[
(x + 1)(x + 2) = x^2 + 2x + x + 2 = x^2 + 3x + 2
\]
2. Now multiply by 2:
\[
2(x^2 + 3x + 2) = 2x^2 + 6x + 4
\]
Thus, the expression \( 2(x + 1)(x + 2) \) simplifies to:
\[
\boxed{2x^2 + 6x + 4}
\]