Apply the properties of operations to determine which expression is equivalent to a+b+c(d+2)

Question

.(1 point)
Responses

a+b+cd+2c
a plus b minus c d minus 2 c

a+b+cd+c
a plus b minus c d plus 2 c

2abcd
2 a b c d

a+b+cd+2

Answer 1

To simplify the expression \( a + b + c(d + 2) \), we can distribute \( c \) to both terms inside the parentheses:

\[ c(d + 2) = cd + 2c \]

Now, substituting this back into the original expression:

\[ a + b + c(d + 2) = a + b + cd + 2c \]

Therefore, the equivalent expression is:

\[ a + b + cd + 2c \]

So the correct response is:

a + b + cd + 2c.