Distributive Property Notes

​Using Tash's approach we get
7(x) + 7(2) We can multiply 7 and x because the 7 is telling us how many x's we have.
7x + 14 We can not combine x's and 14 so stop here

​The distributive property allows the NUMBER outside the parentheses to be DISTRIBUTED to the terms inside the parentheses.

What does distributed mean?

It means to give out or pass out, think "we distributed the notes to everyone" or "I distributed my birthday invitations"

We distribute to ALL terms in the ( )

​Area models can be helpful when distributing.

When making the model you need one row, that is where the number outside the ( ) will go.
The numbers inside the ( ) will tell you how many columns you need. In this case we had 3x and 2, that is 2 terms so we need 2 columns.

​Now using the model find the area of each section. (Area = length X width)

Left Box has the terms 5 and 3x, lets set it up:

5(3x) now multiply the constant 5 and the coefficient 3

15x you have the first term for our expression! Write it in the left box.

​Now using the model find the area of each section. (Area = length X width)

Right Box has the terms 5 and 2, lets set it up:

5(2) now multiply the constant 5 and the constant 2

10 you have the second term for our expression! Write it in the right box.

​15x

And that is it, you are done!

The answer for #2 is

15x+10

**The + came from the 10 being positive

​15x

​10

​We will again multiply the outside number by both terms in the expression, this way we get 2 terms in our answer.
7(x) + 7(-9)
7x + (-63) or 7x - 63

4. The cost (in dollars) of a custom-made sweatshirt is represented by 3n+30, where n is the number of different colors in the design. Write and interpret a simplified expression that represents the cost of 15 sweatshirts.

We need to find the cost of 15 sweaters.

Since n = 15 we can use the expression they gave us. We will replace the variable with 15 then do the math.

3n + 30
3(15) + 30
45 + 30
75

Some addition and subtraction problems look very similar to distributive property problems.

Make sure to read the problems carefully!!