1. Adding and subtracting binomial

2. + + Recap of like and unlike terms Unlike terms Like terms
5 apples + 3 apples
5a a
5 apple + 3 Bananas
5a + 3b
Fruits are same / Same variables
Fruits are different/ Different variables
Unlike terms
Like terms

3. Recap Like terms:- Unlike terms:-
Terms with same variables and powers are Like Terms.
3 x -7 x
Term Term 2
Variable x is present in both the terms and the Power of x is 1.
Unlike terms:-
Unlike terms are two or more terms that do not have same variables and powers.
3 x -7 xy
Term Term 2
Variable x is not present in Term 2 and variables xy is not present in Term 1. Also, the
power of Term 1 is 1 and power of Term 2 is 2.

4. Constant and variables n
Term
Variable
Power
Type
3X and 2X
Same variables x
Same power 1
Like terms
w and
Same variables w
Same power 1
Like terms
5 and 1.8
Same power 0
Like terms
Both are constant
Different variables x2 and x
Unlike terms
5x2 and 2x
Different power 2 and 1
Unlike terms
6a and 6b
Different variables a and b
Same power 1
Constant and variables n
3.2 and n
different power 0 and 1
Unlike terms

5. Addition and subtraction of algebraic expressions
Addition and subtraction of algebraic expressions is nothing but combining like terms or grouping similar objects. x x x x x x x x + = x x x x x x x x x x = 9x 4x + 5x x x x x - = x x x x x x x x = 2x 6x - 4x
To combine like terms having same variables, add or subtract the numerical coefficients.

6. Adding binomials (6a + 3) + (4a +2) = (6a + 4a) + 3 +2
Example 1: Add 6a + 3 and 4a + 2.
Solution: (6a + 3) + (4a + 2)
Like terms
(6a + 3) + (4a +2)
Like terms
Combining Like terms, we get
= (6a + 4a)
= 10a + 5
Ans: 10a + 5

7. Example 2: Add -9pq + 23 and 4pq - 2.
Adding binomials
Example 2: Add -9pq + 23 and 4pq - 2.
Solution: (-9pq + 23) + (4pq – 2)
Like terms
-9pq pq - 2
Like terms
Using integer rule: When both
signs are different, subtract and
put the sign of bigger number.
= (-9pq + 4pq)
= -5pq + 21
Ans: -5pq + 21

8. Example 1: Subtract 21b - 3 from -9b + 12.
Subtracting binomials
Example 1: Subtract 21b - 3 from -9b + 12.
Solution:
Subtract (21b – 3) from (-9b + 12)
(–) (21b – 3) (-9b + 12)
It is given that (21b – 3) has to be subtracted from (-9b + 12). It means that we have to
remove (21b – 3) from (-9b + 12).
From (-9b+12) remove (21b – 3)
(-9b+12) – (21b – 3) (remove means minus)
= -9b + 12 – 21b + 3 (removing brackets)
= -9b – 21b (combining like terms)
= -30b + 15
Using integer rule: When
both signs are same, add
and put the same sign
Ans: -30b + 15

9. Example 2: Subtract -12p2q + 5 from 25p2q – 23.
Subtracting binomials
Example 2: Subtract -12p2q + 5 from 25p2q – 23.
Solution:
Subtract -12p2q + 5 from 25p2q – 23
(–) (-12p2q + 5) (25p2q – 23)
It is given that (-12p2q + 5) has to be subtracted from (25p2q – 23). It means that we
have to remove (-12p2q + 5) from (25p2q – 23).
From (25p2q – 23) remove (-12p2q + 5)
(25p2q – 23) – (-12p2q + 5) (remove means minus)
= 25p2q – p2q – 5 (removing brackets)
= 25p2q + 12p2q – 23 – 5 (combining like terms)
= 37p2q – 28
Using integer rule: When
both signs are same, add
and put the same sign
Ans: 37 p2q – 28

10. Try these Add: 10a + 3 and 6a + 6 14pq – 9 and -12pq + 8 Subtract:
-2pq +9 from 9pq – 2