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

Question

Responses

x2+6x+2
x squared plus 6 x plus 2

2x2+6x+4
2 x squared plus 6 x plus 4

2x2+3x+2
2 x squared plus 3 x plus 2

2x2+5x+2

Answer 1

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

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

2. Now, multiply the entire expression by 2: \[ 2(x^2 + 3x + 2) = 2x^2 + 6x + 4 \]

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

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

Therefore, the correct response is:

2x² + 6x + 4 (or "2 x squared plus 6 x plus 4").