# How do you factor #(r+s)(s+t)-(r+s)(s-t)+(r+s)(s+t)#?

##### 2 Answers

#### Explanation:

To factor this expression, look for a factor that all the terms have in common.

Then you can factor that one out from all the terms.

In this case, all three terms have a factor in common, namely

Factor out

• Be sure to keep the parentheses for the expression you factored out

It's an error to write it like this (without the beginning parentheses)

This means that only the

• Be sure to enclose the expression in brackets

It's an error to write it like this (without the brackets)

This doesn't show that

**Check**

To check factoring, see if distributing the factor brings back the original expression

Distribute

#### Explanation:

#"take out the "color(blue)"common factor "(r+s)#

#rArr(r+s)[(s+t)-(s-t)+(s+t)]#

#"simplifying the terms in the bracket gives"#

#=(r+s)(cancel(s)+tcancel(-s)+t+s+t)#

#=(r+s)(s+3t)#