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

Responses

A) 2x^2+5x+2
2 x squared plus 5 x plus 2

B) 2x^2+3x+2
2 x squared plus 3 x plus 2

C) 2x^2+6x+4
2 x squared plus 6 x plus 4

D) x^2+6x+2

1 answer

To rewrite the expression \(2(x+1)(x+2)\), we first need to expand it.

  1. Start by expanding the binomials: \[ (x + 1)(x + 2) = x^2 + 2x + 1x + 2 = x^2 + 3x + 2 \]

  2. Now, multiply this result by 2: \[ 2(x^2 + 3x + 2) = 2x^2 + 6x + 4 \]

So, the expanded form of the expression \(2(x + 1)(x + 2)\) is \(2x^2 + 6x + 4\).

Therefore, the correct answer is:

C) 2x^2 + 6x + 4.