This document contains a lesson on algebraic operations taught by Md. Abdul Quddus in the Mathematics department. The lesson covers simplifying algebraic expressions using properties like commutative, associative, and distributive properties. It also covers combining like terms. Examples are provided to demonstrate simplifying expressions using these properties and combining like terms. The learning outcomes are listed as being able to simplify equations and find solutions to quadratic equations.

1. Welcome
Md. Abdul Quddus
Department: Mathematics
Campus : 05

2. Chapter : Four
Lesson declaration

3. Today’s lesson
Algebraic operation

4. Learning outcome
At the end of this lesson students will be able. .
 to simplify the equation
 to find the solution of a quadratic equation

5. Simplifying Algebraic Expressions
Commutative Properties
Addition: a b b a  
Multiplication: a b b a  
m r 
12t  
5 y 
8 z 
5y 
8z 
12 t
r m

6. Associative Properties
Addition:    a b c a b c    
Multiplication:    a b c a b c    
  92mr  
  17q r  
 5 3 6   
 2 7 3   
 5 3 6 
 2 7 3  
 17q r 
 92m r 
Simplifying Algebraic Expressions

7. Distributive Property of Multiplication
 a b c ab ac  
 4 6 2x y z  
 5 x y  
 3 2 7x  
5 5x y
6 21x 
4 24 8x y z 
 a b c ab ac  
Simplifying Algebraic Expressions
  km 74 km 74 

8. Simplify each expression by combining like terms.
mm 148  aa6 73 22
 yy
m6 a7 72 2
y
456  zz
z7 1
xxyy  129227
y9 x10 14
 a46
a24
 x98
x72

9.   8325 y
Simplify each of the expressions.
81510 y
   32517  xx
 32577  xx
  1231  yy
1231  yy
132 y
2310 y 151077  xx
223 x

10. Addition and Multiplication Properties
316 x
26 x
mm 4210 
6266 x
8x
m210 
2
2
2
10




m
m5
3
68
a

3
2
a

    3
3
23
a

a6

11. Addition and Multiplication Properties
217716  yy
191y
yy 54104 
11911 y
20y
y14
11
14




 y
y14
 13413  xx
41213  xx
412121213  xxxx
4x
1725 y
217225 y
155 y
5
15
5
5

y
3y

12. Addition and Multiplication Properties
  1026024  x
86084  x
604  x
8684  x
68868684  x
4
60
4
4



 x
15x

13. •Simplify,
4x + 7 – 4 = 3x - 6
Home Work