1. LIKE TERMS DEFINITION:
LIKE TERMS ARE TERMS THAT HAVE THE SAME VARIABLES RAISED TO THE SAME POWERS.
EXAMPLES:
3X AND 4X ARE LIKE TERMS
10Y AND 4Y ARE LIKE TERMS
X2 AND 4X2 ARE LIKE TERMS

2. LIKE TERMS UNDERLINE LIKE TERMS
ADD OR SUBTRACT THE NUMBERS IN FRONT OF THE VARIABLES AND BRING THE VARIABLES DOWN.
IF THERE IS NOT A NUMBER IN FRONT OF THE VARIABLE IT IS UNDERSTOOD TO BE 1 AND YOU SHOULD ALWAYS PUT THE 1 IN THE PROBLEM WHEN YOU COPY IT.

3. LIKE TERMS EXAMPLES: 3X + 4X = 7X 12Y + 11Y = 23Y 2X2 + 3X2 = 5X2
6X + 5X + 1X = 11X + 1X = 12X
3x +2y + 4x + y
3y + 2x + 7

4. LIKE TERMS TRY THIS 2Y + 3Y 4Y3 + 3Y3 XY + 5XY 2X + 3Y
7X + 3Y + 4Z + 6X + Y
3X + 5X2

5. DISTRIBUTIVE PROPERTY
FOR ANY NUMBERS, A, B AND C:
A(B + C) = AB + AC
ANY TIME YOU HAVE A NUMBER TIMES TWO OR MORE TERMS ADDED OR SUBTRACTED INSIDE THE ( ) YOU MUST MULTIPLY THE NUMBER OUTSIDE THE ( ) TIMES EACH NUMBER INSIDE. IT DOES NOT MATTER IF THE NUMBER OUTSIDE IS BEFORE OR AFTER THE ( ).
2(4+ 5) OR (4+5)2

6. DISTRIBUTIVE PROPERTY
EXAMPLE:
6(4 + 2) SINCE THE ( ) CONTAINS TWO NUMBERS YOU CAN USE EITHER ORDER OF OPERATIONS OR DISTRIBUTIVE PROPERTY TO SIMPLIFY.
ORDER OF OPERATIONS
6( )
6(6) 36
DISTRIBUTIVE PROPERTY
6(4) + 6(2)
NO MATTER WHICH WAY YOU DO THE PROBLEM THE ANSWER WILL BE THE SAME.

7. DISTRIBUTIVE PROPERTY
4 ( X + 6) SINCE THE ( ) CONTAINS A VARIABLE AND A NUMBER THAT ARE NOT LIKE TERMS YOU MUST USE DISTRIBUTIVE PROPERTY IN ORDER TO SIMPLIFY.
4( 1X + 6)
4 (1X) + 4(6)
4X + 24

8. DISTRIBUTIVE PROPERTY
EXAMPLE:
5(2X + 3Y)

9. DISTRIBUTIVE PROPERTY
EXAMPLE:
3( 4X – 5)

10. DISTRIBUTIVE PROPERTY
EXAMPLE:
7( X + Y + 4 )

11. DISTRIBUTIVE PROPERTY
6( 3X + 4Y + 2X )

12. DISTRIBUTIVE PROPERTY
( 2X + 4 ) 6

13. DISTRIBUTIVE PROPERTY
3( 2X + 4 ) +5x

14. LIKE TERMS 5-MINUTE CHECK
3X + X
2X + 3Y + 4X + Y + 7
4Y + 2X + 3
4. 5X³ + 3X³
5. 2X + 2X² + 3X²

15. DISTRIBUTIVE PROPERTY 5-MINUTE CHECK
6. 4( X + 6)
( 4X + 3Y + 4 )
8. 7( 2X X )
9. ( 3X + 5 ) 9
( 4X – 3Y – 4 )
11. 2X +7(X + 3)