I am doing a homework using distributive properties, I never really got shown how to subtract equations using distributive properties, someone help, please?

Question

I know how to do equations, like so

 

6(n + 4)

 

Once i have simplified the equation it looks like this,

(6 x n) + (6 x 4)

Answer 1

Hm. Is the problem something like   4(n-10)  ?

 

Distribution is something you've been doing ever since you started doing multiplication with two digits, like:

 

42

x5

---

210

 

You first multiply the 5 times the 2 = 10, then the 5 times the 40 = 200 and you add the two together. And we shorten this by using carrying and pretending the 40 is a 4.

 

You could rewrite this multiplication problem as 5(40 + 2) ... which looks a lot more like how you're taught distribution. Then you would multiply the 5 times the 40 and the 5 times the 2 and add the two results together. This gives you exactly what you got in your 42 x 5 problem. 210.

 

So, what if I write an algebra distribution problem vertically? You have ((note: I'm using * for my times sign)):

 

N + 7      First multiply the 7 * 5 and write 35 below the 7.

*    5       Second multiply 5 * N and write 5N below the N.

------

5N + 35   This is conceptually a lot easier than doing the distribution in a line, but it's the same thing.

 

Now let's use a - sign between the two. The only difference is that you have to remember your positive and negative math.

 

N - 12   First multiply 4 *-12. Positive times negative is negative, so it's -48.

*    4    Second, multiply 4 * N and get 4N

-------

4N - 48 

 

This is exactly the same as 4(N-12) = (4 * N) + (4 * -12) = 4N - 48. 

 

Doing the problem vertically often makes more sense to my students.

 

--Louise