2g+3(g+5)=

Question

Simplify each expression. Justify each step.

Answer 1

Normally, you'd compute what's in the parenthesis first, right? We do this because of the order of operations. If you don't know what that is, you should consider reviewing that first (I'd be happy to schedule a lesson if you need a little help!).

 

However, we can't actually do that because what's in the parenthesis are not like terms and you can't add unlike terms - "g" is a variable and 5 is a number.

 

So instead we're going to use what's called the DISTRIBUTIVE LAW. The distributive law says that distribute that 3 to each number in the parenthesis. In other words, we're going to multiply what's right outside the parenthesis by EACH of the things in the parenthesis SEPARATELY.

 

2g + (3*g) + (3*5)

2g + 3g + 15

 

 

Next, you combine like terms by adding their coefficients (the number directly in front of the variable).

5g + 15

Answer 2

2g + 3(g + 5)          distribute the 3

2g + 3g + 3(5)        combine like terms

5g + 3(5)                simplify

5g + 15