Apply the properties of operations to determine which expression is equivalent to a+b+c(d+2) .(1 point)

Question

Responses

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

2abcd
2 a b c d

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

a+b+cd+2c
a plus b minus c d minus 2 c
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Answer 1

To determine which expression is equivalent to a+b+c(d+2), we can simplify each expression step by step:

1) a+b+cd+c: This expression does not simplify to a+b+c(d+2). It includes an additional term of "c" outside the parentheses.

2) a plus b minus c d plus 2 c: This expression does not simplify to a+b+c(d+2). It includes an additional term of "c" outside the parentheses and subtracts "cd".

3) 2abcd: This expression does not simplify to a+b+c(d+2). It includes "abcd" which is not equivalent to "(d+2)".

4) a+b+cd+2: This expression does not simplify to a+b+c(d+2). It includes an additional term of "2" outside the parentheses.

5) a plus b minus c d minus 2 c: This expression simplifies to a+b+cd+2c. By distributing the "c", we get "cd+2c", which is equivalent to "(d+2)c".

Therefore, the correct expression that is equivalent to a+b+c(d+2) is:

a+b+cd+2c