COMBINING LIKE TERMS

WHAT IS A TERM?

• A PART OF AN EQUATION OR EXPRESSION

• COEFFICIENT- A NUMBER USED TO MULTIPLY A VARIABLE

• CONSTANT- A NUMBER ON ITS OWN

3X-4=9Term Term Term

Coefficient

Constants

EXAMPLE

7Y-2+9X=13TERMS:

COEFFICIENTS:

CONSTANTS:

VARIABLES:

7y, -2

, 13

7

-2, 13Y

, 9x

, 9

, X

WHAT EXACTLY DOES THE SAME OR “LIKE” MEAN?• TERMS WITH THE SAME VARIABLE OR

VARIABLES AND RAISED TO THE SAME POWER

SAME: 5X AND 12X

SAME: 10 AND 7

SAME: 9Z AND 14Z

SAME: 8Y

5x, 8y, 9z, 10, 12x, 14z, 7

DOCUMENT CAMERA

• I COULDN’T FIND A VERY FUN VIDEO BUT I DID REALLY LIKE THE WAY THE WOMAN EXPLAINED THE CONCEPT IN THESE VIDEOS SO I THINK I’LL JUST USE THE DOCUMENT CAMERA TO DO A SHORTER VERSION OF WHAT SHE DID IN THESE FOLLOWING VIDEOS

• HTTP://WWW.VIRTUALNERD.COM/ALGEBRA-1/ALGEBRA-FOUNDATIONS/SIMPLIFYING-EXPRESSIONS/SIMPLIFYING-EXPRESSIONS-EXAMPLES/LIKE-TERMS-DEFINITION

• HTTP://WWW.VIRTUALNERD.COM/ALGEBRA-1/ALGEBRA-FOUNDATIONS/SIMPLIFYING-EXPRESSIONS/SIMPLIFYING-EXPRESSIONS-EXAMPLES/ADD-LIKE-TERMS-EXAMPLE

WHAT IS COMBINING LIKE TERMS

• IF NUMBERS HAVE A VARIABLE, THEN YOU CAN COMBINE ONLY ONES THAT HAVE THE SAME VARIABLE

• ALSO IF NUMBERS DON’T HAVE VARIABLES THEY CAN ONLY BE COMBINED WITH OTHER NUMBERS THAT DON’T HAVE VARIABLES

• LIKE TERMS COULD BE COMBINED BY ADDING THEIR COEFFICIENTS

HOW TO COMBINE LIKE TERMS

• FIRST, CHANGE OUR OPERATORS TO ADDITION BY USING KEEP-CHANGE-CHANGE

• SECOND, REORDER THE EXPRESSION SO LIKE TERMS ARE NEXT TO EACH OTHER

• FINALLY, COMBINE LIKE TERMS BY ADDING THEIR COEFFICIENTS (SIMPLIFY)

Combine like terms

By combining apples with apples and oranges with oranges, you get...

+

1 apple

3 apples + 2 oranges +(- 2) apples + 2 oranges

+ 4 orangescoefficients

+ – +

+ +( – ) +

EXAMPLE

=4 +2 +(-2 )+(-1 ) = + +

+

4 + 2 -2-1

= + =2 +1

CHANGE EVERYTHING TO ADDITION

2X + (-3Y) + 5X + 3Y + 12REORDER YOUR TERMS

2X+5X+(-3Y)+(3Y)+12FIND THE LIKE TERMS

2X +5X +(-3Y) +3Y +12COMBINE LIKE TERMS

7X +12

Example: Simplify 2x - 3y + 5x + 3y + 12

Remember: adding the

opposite cancels out so

(-3x)+(3x)=0

SIMPLIFY:

Reorder the terms

Combine like terms (simplify)

4x2-13y+4x+12x2-3x+3

4x2 +12x2+ 4x +(-3x)+(-13y)+3

16x2 + x + (-13y) + 3

Change all operations to addition using keep-change-change

4x2 +(-13y) +4x +12x2 +(-3x) +3

Combine like terms

Identify like terms.

Combine coefficients: 14 – 5 = 9

A. 14a – 5a

9a

Change any subtraction to addition

14a +(-5a)Reorder Terms

B. 7y + 8 – 3y – 1 + y

Combine like terms

Change any subtraction to addition

7y +(-3y)+y

Identify like terms ; the coefficient of y is 1, because 1y = y.+8 +(-1)

Combine coefficients: 7 – 3 + 1 = 5 and 8 – 1 = 7

Reorder Terms

5y + 7

7y +8 +(-3y) +(-1) +y

3q

C. 4q – q

Identify like terms ; the coefficient of q is 1, because 1q = q.

Combine coefficients: 4 +(-1) = 3.

4q +(-1q)

Combine like terms (on the boards).

Change any subtraction to addition

Reorder Terms

D. 5c + 8 – 5c – 2

6

Combine like terms (on the boards).

5c +(-5c) +8 +(–2)

Combine coefficients: 4 +(-1) = 3.

Change any subtraction to addition

Identify like terms ; the coefficient of q is.

Reorder Terms

5c + 8 +(-5c) +(–2)

F. 5m2 – 7m – 8 + 4

5m2 – 7m – 4

Combine like terms (on the boards).

Combine coefficients: 4 +(-1) = 3.

Change any subtraction to addition

Identify like terms ; the coefficient of q is.

Reorder Terms

5m2 +(-7m) + (-8) + 4

5m2 +(-7m) +(-8) +4

E. 4m + 9n – 2

4m + 9n – 2

No like terms.

Combine like terms (in your notes).

Combine coefficients.

Change any subtraction to addition

Identify like terms ; the coefficient of q is.

Reorder Terms

4m +9n +(-2)