Combining Like Terms to Write Equivalent Expressions

Question 1

_________ terms are terms that have the same variable raised to the same power. ex. 10m and 6m or 7z 2 and 3z 2 Remember, if a variable appears more than once in an expression, that variable refers to the _________ number each time it is used. Like terms can be added and subtracted. ex. 10m + 6m = 16m 7z 2 -3z 2 = 4z 21.) When simplifying expressions, FIRST look to see if you can use the distributive property. 2.) Next, combine like terms by adding or subtracting. Pay attention to the operation signs. 3.) All leftover numbers that aren’t attached to any variables (constants) are also considered like terms. Look at their signs to see if you should add or subtract them.

Answer 1

LIKE terms are terms that have the same variable raised to the same power. ex. 10m and 6m or 7z 2 and 3z 2 Remember, if a variable appears more than once in an expression, that variable refers to the SAME number each time it is used. Like terms can be added and subtracted. ex. 10m + 6m = 16m 7z 2 -3z 2 = 4z 21.) When simplifying expressions, FIRST look to see if you can use the distributive property. 2.) Next, combine like terms by adding or subtracting. Pay attention to the operation signs. 3.) All leftover numbers that aren’t attached to any variables (constants) are also considered like terms. Look at their signs to see if you should add or subtract them.

Question 2

Ex. 8n 2+ 5 – n 2+ 9

(Since you can’t use the distributive property, combine like terms with variables first. You may want to color-code them!)

8n 2– 1n 2= ____ + 5 + 9 = ____ _________

(Now put both parts together for your answer!)

• Arrange your answer in order from variables with the highest powers to the lowest powers, and then write your constants last.

Answer 2

Ex. 8n 2+ 5 – n 2+ 9 (Since you can’t use the distributive property, combine like terms with variables first. You may want to color-code them!)

8n 2– 1n 2= 7n 2 + 5 + 9 = +14

(Now put both parts together for your answer!)

• Arrange your answer in order from variables with the highest powers to the lowest powers, and then write your constants last.

Question 3

Ex. 3(4a + 5) – 6 + 8a

(Use the distributive property and drop down the rest.)

___ + ___ – 6 + 8a
(Now combine like terms with variables.) ___________ (Now combine your constants, numbers.) __________ (Answer!)

Answer 3

Ex. 3(4a + 5) – 6 + 8a

(Use the distributive property and drop down the rest.)

___ + 15 – 6 + 8a
(Now combine like terms with variables.) ___________ (Now combine your constants, numbers.) __________ (Answer!)

Question 4

Ex. q 3+ r 3+ q 2+ 10 – 2 ________________
None of these variables are like because they either have a different letter or the same letter with a different exponent. So, therefore, you cannot combine any of them. Just combine the constants (numbers).

Answer 4

Ex. q 3+ r 3+ q 2+ 10 – 2 = q+ r 3 +q 2 + 8
None of these variables are like because they either have a different letter or the same letter with a different exponent. So, therefore, you cannot combine any of them. Just combine the constants (numbers).

Question 5

Now simplify these! I recommend either color-coding them or shape-coding the like terms. Try to use the distributive property first, if it applies. Then combine like terms.

1.) 5w 3+ 8 – 4 + 2w 3

2.) a 2+ 3 + 7a 2-1 + b

Answer 5

Now simplify these! I recommend either color-coding them or shape-coding the like terms. Try to use the distributive property first, if it applies. Then combine like terms.

1.) 5w 3+ 8 – 4 + 2w 3
7w 3

2.) a 2+ 3 + 7a 2-1 + b
8a 2 b + 2

Question 6

3.) 6g 2+ 2(3h 3+ 1) – 4g 2+ h 3

Answer 6

3.) 6g 2+ 2(3h 3+ 1) – 4g 2+ h 3
3 x 2+4y+2

Question 7

4.) 18x 2+ 5y + 4 – y – 15x 2– 2

Answer 7

4.) 18x 2+ 5y + 4 – y – 15x 2– 2
3 x 2+4y+2

Question 8

5.) 4(5m + 2) – 8 + 3m

Answer 8

5.) 4(5m + 2) – 8 + 3m
20m-8-8+3m
23m