Solve (-2x-3)4. Simplify by using distributive property

Answer 1

Hello Ella,

I am going to give you the assistance you require for the problem by giving you the solution first. As a tutor, however, I feel a responsibility to explain the distributive property to you so that it may be of assistance to you in the future.

So, the problem you present is as follows:

(-2x - 3)4

The answer is as follows:

-8x - 12

Please note what we did here: We multiplied each term inside the parentheses by the term outside of the parentheses. We could have just as easily re-written the expression as follows:

4(- 2x - 3) We still would have had the answer of - 8x - 12, right? Okay. But why you might find yourself asking. Because all we are doing is taking the term outside the parentheses and multiplying it by the term outside the parentheses, while paying attention to the sign - that is, whether each term is positive or negative.

Now for the additional information I promised you. If you find it of value, great. If not, just ignore, okay?

The Distributive Property is first of all; a law in mathematics. Second, the distributive property says this:

Distributing a multiplier over a sum of numbers will provide the same answer as multiplying each term by the multiplier and adding it together. The term I speak of is called the "addend."

Here is an example: Lets assume you have two friends who love ice cream. It is a hot summer day and the first friend, Jennifer goes to get some ice cream. She orders a cone with 2 scoops of ice cream, okay?

We can express Jennifer as 1(2), correct? She is one person, who purchased two scoops of ice cream.

Now imagine your other friend, David, goes in to the ice cream shop and purchases a triple ice cream cone (a cone with three dips of ice cream). We can express this mathematically, can't we? Do you know how to do so?

The answer is 1(3) because David is one person who purchased three scoops.

Now, imagine that both David and Jennifer go to get ice cream at the exact same time meaning together.

Imagine that Jennifer orders the exact same as the previous example; she purchases a double ice cream cone, with two scoops of ice cream. Then imagine David orders the exact same as he did in the previous example which is one cone with three dips of ice cream. Explained as above we can express the two examples mathematically.

Remember: In the first example it was 1(2) to express Jennifer's purchase and 1(3) to express Davod's. In the first example, they went separately, right? Now look at what changes when we put them together to purchase the exact same purchase:

Since we have two people purchasing ice cream, we would have 2 as one term (one for each person, right)? Then we would add the total number of scoops of ice cream. When we do so we know that between the two of them, they purchased a total of five scoops, right? So now the mathematical expression to represent this purchase is 2(2 + 3) = 4 + 6 = 10, correct? When we calculate the second example - since two friends are going to get a total of 6 scoops we would be able to use the following represent the purchase 2(3 + 3) = 6 + 6 = 12

The above provides you - hopefully - with an explanation of what the distributive law of math means.,

I hope I have assisted you. I apologize for the length of the entire explanation however I want to be sure you understand the concept. If you want further clarity, want to ask an additional question, or simply wish to leave feedback, please click the "add comment" prompt and place the information below this solution. Finally, should you need one on one tutoring, please feel free to reach out to me or any of our highly qualified expert tutors. Best.