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

A. x²+6x+2
B. 2x²+3x+2
C. 2x²+5x+2
D. 2x²+6x+4

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. First, expand \( (x+1)(x+2) \): \[ (x+1)(x+2) = x^2 + 2x + x + 2 = x^2 + 3x + 2 \]

  2. Next, 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: D. \( 2x^2 + 6x + 4 \).