Middle School Math Solutions – Expand Calculator, Distributive Law

The distributive law helps with multiplication problems by breaking down large numbers into smaller numbers. In this blog post, we will talk about the distributive law and how to use it.

The law says that multiplying a number by a group of numbers added together is the same as multiplying each separately. What does this mean? Here we can see it in a formula:

You can see that the multiplication of a has been distributed among the sum of b and c.

Let’s see some examples of how to use the distributive law.

First example (click here):

                                                                Expand 4(2x+5)

1. Define the values for a, b, c

                                                               a=4,   b=2x,   c=5

Refer to the formula to see what these values are.

2. Plug these values into the distributive law formula

                                                               4(2x+5)=4∙2x+4∙5

3. Simplify your answer

                                                                4∙2x+4∙5=8x+20

8x+20 is our answer.

Next example (click here):

                                                                Expand 5(10-9p)

1. Define the values for a, b, c

                                                              a=5,   b=10,   c=-9p

2. Plug these values into the distributive law formula

                                                            5(10-9p)=5∙10+5∙(-9p)

3. Simplify your answer

                                                             5∙10+5∙(-9p)=50-45p

50-45p is the answer.

In this last example, we will see another application of the distributive law.

Last example (click here):

                                                                     5(106)

Just by looking at this problem, this might be difficult to calculate quickly. So let’s use the distributive law.

1. Make 106 the sum of two numbers

                                                                 106=100+6

2. Plug this in for 106

                                                                  5(100+6)

3. Define values a, b, c

                                                            a=5,   b=100,   c=6

4. Plug these into the distributive law formula

                                                           5(100+6)=5∙100+5∙6

5. Simplify your answer

                                                         5∙100+5∙6=500+30=530

530 is the answer.

As you can see, the distributive law is very handy. Therefore, I highly suggest you memorize this formula and become familiar with how to use it. You can do so by doing as many examples as you can. For practice examples and more help, check out Symbolab’s Practice

Until next time,

Leah