# Applying the Distributive Property

The distributive property is a source of many mistakes in algebra. When a negative sign, multiplication, or division is next to a set of parentheses, everything inside the parentheses will be affected.

The answer shown below is wrong.  Try working your way through the problem backwards, from the answer up. As you find each mistake, try to identify the thinking behind it… what perspective led to the mistake? What should have been done instead?

$(-2)(3-c)+(-2+5c-4d)-3(-d-c+1)$

$=-(6-2c)+(-2+5c-4d)-(3d+3c+3)$

$=-6-2c-2+5c-4d-3d+3c+3$

$=-8c-7c-7d+3c+3$

$=-c-7d+3c+3$

$=2c-7d+3$

.

..

Hint 1: the correct answer to the original problem is: $10c-d-11$

Hint 2: there are mistakes made between all pairs of lines except the last pair.

### Whit Ford

Math tutor since 1992. Former math teacher, product manager, software developer, research analyst, etc.

## 2 thoughts on “Applying the Distributive Property”

1. Harold says:

Shouldn’t the answer be: 10c – d – 11?

1. Harold,

You are correct… Thank you! I have fixed the answer in the post.

I must not have been thinking very clearly when I made the original posts, and I am rather startled that nobody has caught those mistakes until today. Well done, and thanks again!