# Simplify :  1. 10y + 2b + 3y = ?  2. 6m  + n + 5m = ?  3. 4a + 3b - a = ?  4 . 3q + 2b - 3b = ?  5. 4t + 7 - 2t = ?  6.4y + 8 - 2 + 3y = ? ?

Relevance

1. 10y+3y+2b= 13y+2b

2. 6m+5m+n= 11m+n

3. 4a-a+3b= 3a+3b

4. 3q+2b-3b = 3q-b

5. 4t-2t+7 = 2t+7

6. 4y+3y+8-2 = 7y+6

• For each expression you collect like terms.  Like terms have the same letters and number of exponents.  Think of the letters as place values in Arithmetic.  You add, subtract the same place values.  You add 10's to 10's, 100's to 100's, etc. Arithmetic deals with specific numbers and algebra deals  with generic numbers.  As an example x can be a 1, a 10 , a 100, etc. And if you have a 5x you know that you have 5 of whatever value x represents.

Until you fully grasp the concept the best method is to rewrite the expression with like terms together. By convention the letter (variable) is listed first.

6.4y + 8 - 2 + 3y = ?

6.4y + 3y + 8 -2 = ?

9.4y + 6  = ?

Since you don't know the numerical value of y you have simplified the expression and can do nothing more.

• I'll do the first one:

10y + 2b + 3y

You want to "combine like terms".  This is like saying, "you have 10 apples, 2 oranges, and 3 more apples".  You end up with "13 apples and 2 oranges" so:

13y + 2b

A mathematically way to show this is that since we're adding all numbers we can do it in any order, so group the y's (subtracting is just adding the opposite, so don't lose track of your signs)

10y + 3y + 2b

Factor out the y:

(10 + 3)y + 2b

Simplify:

13y + 2b

All others are done the same way, just more of the same with different numbers.  You work on those having learned from the above.