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

Question

Responses

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

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

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

2x2+5x+2
2 x squared plus 5 x plus 2

Answer 1

To rewrite the expression \( 2(x+1)(x+2) \), we first expand the expression inside the parentheses:

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

Now we multiply this 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 corresponding response from your options is:

2x² + 6x + 4.