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

Answer 1

To apply the properties of operations to determine which expression is equivalent to a+b+c(d+2), let's first expand the expression using the distributive property:

a + b + c(d + 2)
= a + b + cd + 2c

Now, let's look at the properties of operations:

1. Commutative property of addition: The order of the terms can be changed without affecting the result.

2. Associative property of addition: The grouping of the terms can be changed without affecting the result.

3. Associative property of multiplication: The grouping of the factors can be changed without affecting the product.

Based on these properties, we can rearrange the terms in different orders or change their groupings.

For example, we can change the order of terms using the commutative property of addition:

a + b + cd + 2c = a + cd + 2c + b

We can change the grouping of terms using the associative property of addition:

(a + cd) + (2c + b)

Similarly, we can change the grouping of factors using the associative property of multiplication:

(a + c)(d + 2)

Therefore, the expression equivalent to a + b + c(d + 2) can be written as (a + c)(d + 2).