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What is another way to write the expression 2(x+1)(x+2)?

A. x^2 + 6x + 2
B. 2x^2 + 6x + 4
C. 2x^2 + 3x + 2
D. 2x^2 + 5x + 2

1 answer

To rewrite the expression \(2(x+1)(x+2)\), we can first expand the expression inside the parentheses and then distribute the 2.

  1. Expand \((x+1)(x+2)\):

\[ (x+1)(x+2) = x^2 + 2x + x + 2 = x^2 + 3x + 2 \]

  1. Now, multiply the result by 2:

\[ 2(x^2 + 3x + 2) = 2x^2 + 6x + 4 \]

So, the expression \(2(x+1)(x+2)\) can be rewritten as:

\[ 2x^2 + 6x + 4 \]

The correct answer is:

B. \(2x^2 + 6x + 4\)