COMBINING LIKE TERMS

1. COMBINING LIKE TERMS

2. People who are identical twins are a “like pair” because they have the exact same features. An Algebraic Equation we can write for this is: t + t = 2t One Twin + One Twin = 2 Twins. In Algebra we call this: “Combining Like Terms”.

3. terms- parts of an expression separated by an addition (+) or subtraction (-) sign. Example: 34g + 18 – 3p + 4s This expression has ____ terms 4 like terms- terms that contain the samevariable/sameEXACTgroups of variables. Example: 2b + 3b 2b and 3b are LIKE terms because they both have the variable “b” in them Please Note: 2ab and 3b are not like terms, because one has an a in it.

4. Consider these two expressions: 8x + 7x • LIKE TERMS 8x + 7xy  UNLIKE TERMS

5. Decide if the terms in each pair of items are “Like Terms” or “Unlike” • 1) 4g and 4h ______ • 2) 3h and 5h ______ • 3) 5x and 4xy ______ • 4) 8rp and 7rp ______ • 4g and 4y_______ • 2c and 20c______ • y and 6y______ • 2ab and 6ba ______ Unlike (don’t have the same variable) Like (have the same variable) Unlike (don’t have the same exact variables) Like (have the same exact variables) Unlike (don’t have the same variable) Like (have the same variable) Like (have the same variable) Like (have the same variables)

6. A typical algebraic expression is : 2a + 3b + 3a +4b We can think of “a” as being Apples and “b” as being Bananas, That expression can be represented as: We can combine the like objects. The above can be simplified to be 5 Apples and 7 Bananas. Which in Algebra is: 5a + 7b 2a + 3b + 3a + 4b = 5a + 7b

7. Often in real life, it is necessary to combine like items together to create a shorter list of items we can deal with. For example, a family orders food from Burger King. Here is the order: Using Algebra we could write it as: 2b + 1f + 1d + 3b + 2f + 2d If we combine like items, we get a simplified list as follows: 5b + 3f + 3d

8. When combining like terms we combine everything that is the same: 3x + 4x + 8y - 5y 7x 3y So our solution is: 7x + 3y

9. Here is an expression containing 4 terms with two sets of LIKE terms: 6y 3x + 4y + 2x + 2y 5x 5x + 6y

10. Practice 11e 6b + 3e + 7b + 8e 13b 13b + 11e

11. Practice 9y 13z + 3y + 9 + 6y + 7z 20z 20z + 9y + 9

12. We can Subtract Like Terms Also. Suppose that we have bought 5 apples and 6 bananas, But we eat two bananas before putting our fruit into the bowl. The Algebra is: 5a + 6b – 2b (6 bananas take away 2 is 4) 5a + 4b

13. 7e 6b + 9e -3b - 2e 3b 3b + 7e

14. 13z 13y + 14z -y – z 12y 12y + 13z

15. 11 24b + 15 -12b + 10c - 4 – 8c 12b 2c 12b + 11 + 2c

16. WARNING: Like Terms are only used for Adding andSubtracting algebraic terms. We never use combining like terms for Multiplying and Dividing !

20. TRY SOME OUT! 1) 3b – 2b + 4b 5b 2) 4y + 3 – y + 4 3y + 7 3) 5v – v + 6 - 2 4v + 4 4) 3x – 2x + 4y + 2y x + 6y

21. Solve for b. 2b + 3b = 25

22. Solve for b. 12b - 3b = 27

23. Solve for b. 4b + 10 + b - 2 = 18

24. Solve for b. 5b + 2 - b - 12 = 18

25. Solve for b. 5b + 2b - b - 12 = 18

26. Solve for b. 32= 5b + 4b - b - 12

27. Solve for b. 100= 5b +10 + b - 20