Question

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

Answer 1

Answer:  $-13c+13d$

Step-by-step 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:

$=-13c+13d$