Question

Translate the given phrase into an algebraic expression and simplify if possible: the product of -13 and the difference of c

and d.
Note: Enter only the simplified result.​

Answer 1

Answer:
`-13c+13d`

Explanation:

For this exercise it is important to remember the following:

1. By definition, the "Product" is the result of a multiplication.

2. The "Difference" is defined as the result of a subtraction.

3. The Distributive property states that:

`a(b+c)=ab+ac\\\\a(b-c)=ab-ac`

Keeping the above on mind, you know that:

"The difference of
`c` and
`d`" can be represented with the following expression:

`c-d`

Therefore, "The product of -13 and the difference of
`c` and
`d`" can be represented with this expression:

`-13(c-d)`

Finally, you must apply the Distributive property in order to simplify the expression. You get:

`=-13c+13d`