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Notes
Combining Like Terms
One way to simplify an expression is to “combine like terms.”
What does it mean to combine like terms?
You can only combine terms that have the same _______________________ and the same
______________________________._
To combine like terms, first use the commutative property to move all like terms together. Then , combine the coefficients of the variables. Example 1:
2a + 3b – 4a
2a – 4a + 3b
Example 1:
14m – 3n^2 – 2n^2 + 3m
Example 1:
5x + 4x – 6 + 5x^2
_Note: all of your answers should be arranged so that the variables are in ___________________
order first, then in order from greatest to least ___________________________.
Watch out for the following common mistakes! Circle the mistakes below: Mistake #1:
a^2 – 4a + 5a
2a^2
You can ONLY combine terms when the variable has the same exponent.
Mistake #2:
3y + 4x^2 – 3y + 5y
3y – y + 5y + 4x^2
7 y + 4x^2
You should ALWAYS put the variables of your answer in alphabetical order, then in order by exponent.
Mistake #3:
3h + 14g – 5h + 5g
3h + 5h + 14g – 5g
8h + 9g
9g + 8h
You should ALWAYS move the negative sign along with the term that is after it.
Note: Make sure to move any negative signs with the term it is before!
Learning Activity: Combining Like Terms Cards
Cut out the pieces along the dotted lines. Each row is a separate expression. Use these cards on a board or projector to physically move the terms so that like terms are together. This, along with color coding like terms, can help struggling students to see what you are doing when you combine like terms. (This activity can be easily extended by giving each student an index card and asking them to write a term using the variables a, b, or a constant. For example, a student might come up with 3a, 11b or 8. Then choose student cards at random from the room to put together into an expression and solve.)
4a
+ 3a - 16a + a
6b - 7b + 8 + 4b
11 - 19 + 8g - 6g
5g
+ 6g - 4g + 8g
17x - 6y + 9y
- 8x
6y + 8 - 6y - 8
- 6d + 5c - 4c
+ 3c
2a + 8 - a + 4a
2x
+ 5x
- 6x
+ x
4p + 3np - 3n + 2p
Practice
Combining Like Terms Puzzle
Simplify each expression by combining like terms. Find the answer at the bottom of the page. Then write the letter on the appropriate line below to spell out a secret message. (Some letters may be used more than once!)
Did you hear the one about the acupuncture?
_____ _____ _____ _____ _____ _____ _____ _____ _____
_____ _____ _____ _____ _____ _____ _____ _____!
- 2m + 3m^2 - 4m 2. 2x + x – 4y 3. 2m + 4m – 3m^2 4. 2y + 14x – 7x + 9y
- 8n – 4n^2 + 8n 6. 11g – 9g + 8g 7. 3m^2 – 2m + 4m 8. 20 + 10q + 3q – 4
- 4xy + x + 2xy 10. 6m^2 + 6m – 9m^2 11. 3n – 6mn + 2n 12.^3 / 2 x – y + ½x + 3y
- y + x + y + x 14. 8n + 4n^2 – 8n 15. 5 + 5mn – 11mn 16. 15y + 6y – 3x + xy
- 3xy – 5xy + 21y
I. 3m^2 – 2m S. - 4n^2 + 16n E. – 2xy + 21y O. - 6mn + 5 T. 3x – 4y
N. - 3x + xy + 21y W. - 3m^2 + 6m J. 3m^2 + 2m B. x + 6xy A. 10g
A. 7x + 11y E. - 6mn + 5n A. 13q + 16 L.2x + 2y D. 4n^2
Enrichment Activity 1
Combining Like Terms
Have you ever heard the phrase “you can’t compare apples and oranges?” Place each of the terms below on the proper “tree” that contains like terms. (Not all terms belong on a tree!)
x
2 11 4z xy y
9y 2z 2y
3 5z 11y
9x 6x
2 9y 2z 19
7 - x
2 3y 2x 7z
x
8 z
y
