What is another way to write the expression 2(x+1)(x+2)?(1 point)
Responses
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
2 x squared plus 5 x plus 2
x2+6x+2
x squared plus 6x plus 2
To determine which expression is equivalent to 2(x+1)(x+2), we can use the distributive property.
First, distribute the 2 to each term inside the parentheses:
2(x+1)(x+2) = 2 * x * (x+2) + 2 * 1 * (x+2)
This simplifies to:
2x(x+2) + 2(x+2)
Next, distribute the 2x and 2 to each term inside the second set of parentheses:
2x(x+2) + 2(x+2) = 2x^2 + 4x + 2x + 4
Combine like terms:
2x^2 + 6x + 4
Therefore, the equivalent expression for 2(x+1)(x+2) is 2x^2 + 6x + 4.
To write the expression "2(x+1)(x+2)" in another way, you can use the distributive property to multiply the terms:
First, multiply 2 with both terms inside the first parenthesis:
2(x) + 2(1) = 2x + 2
Next, multiply 2 with both terms inside the second parenthesis:
2(x) + 2(2) = 2x + 4
Finally, combine the terms:
2x + 2 multiplied by (x+2) = 2x(x+2) + 2(x+2) = 2x^2 + 4x + 2x + 4
So, another way to write the expression is: 2x^2 + 6x + 4.