1. Logylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Std-9 th sub -Algebra Topic - Algebraic Expression

2. Logylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Std-9 th sub -Algebra Topic - Algebraic Expression Std-9 th sub -Algebra ALGEBRAIC EXPRESSIONS

3. Logylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Std-9 th sub -Algebra Topic - Algebraic Expression Std-9 th sub -Algebra A symbol having a fixed numerical value is called a constant. A symbol which may be assigned different numerical values is called a variable. ALGEBRAIC EXPESSIONS : An algebric expression is a combination of constants and variables connected by some or all the sings of operations lick +,-, *and /.

4. Logylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Std-9 th sub -Algebra Topic - Algebraic Expression Std-9 th sub -Algebra TERMS OF AN ALGEBRIC EXPRESSIONS: The serveral parts of an algebric expression are separated by + or – sings. Each part along with its sings is called the terms of the expression COEFFICIENT : The numerical factor of the terms is called the coefficient of the term.

5. Logylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Std-9 th sub -Algebra Topic - Algebraic Expression Std-9 th sub -Algebra 3.1 OPRATIONS ON ALGEBRAIC EXPRESSIONS: Addition and subtraction of algebraic expressions. Terms with same variables and having same powers are like terms. Solved examples: Add 2a + 3b-15c and 4a-7b+8c. 2a+3b-15c 4a-7b+8c 6a-4b-7c

6. Logylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Std-9 th Sub-ALGEBRA Topic- ALGEBRAIC EXPREESION Std-9 th Sub-ALGEBRA MULTIPLICATION OF ALGEBRAIC EXPRESSIONS. Solve example: (2a+3b)(3a+4b)=2a(3a+4b)+3b(3a+4b ) = +8ab+9ab+ = +17ab+ Exercise 3.1 Add the following expressions: (1)2a+b+7; 4a+2b+3 =6a+3b+10 (2a+b+7)+ (4a+2b+3) =2a+b+7+4a+2b+b+7+3 =2a+4a+2b+b+7+3

7. Logylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Std-9 th sub -Algebra Topic-algebraic expression Std-9 th sub -Algebra 3.2 Factorization of an algebraic expretion ( a) By taking out the common factores: Factorise : 5x+20y Solution :5x+20y=5(x+4y) here 5 and (x+4y)are the factores of 5x +20y. B ) by grouping Factorise :ax+by+bx+ay Solution : ax + bx + ay +by =ax+bx+ay+by =x(a+b)+y(a+b) =(a+b) (x+y)

8. Logylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Std-9 th sub -Algebra Topic-algebraic expression Std-9 th sub -Algebra c) Factorise of difference of two squares: Exercise 3.2 factorise the following. 1. 4x-8y 4x-8y =4(x-2y)

9. Logylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Std-9 th sub -Algebra Topic-algebraic expression Std-9 th sub -Algebra Factors of sum and difference of two cubes.

10. Logylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Std-9 th sub -Algebra Topic-algebraic expression Std-9 th sub -Algebra Exercise 3.3

11. Logylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Std-9 th sub -Algebra Topic-algebraic expression Std-9 th sub -Algebra

12. Logylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Std-9 th sub -Algebra Topic-algebraic expression Std-9 th sub -Algebra Solution : Since 2*5=10 and 2+5=7 Exercise 3.4 Factorise the folloving : 1.

13. Logylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Std-9 th sub -Algebra Topic-algebraic expression Std-9 th sub -Algebra g) Factorise of algebraic expression reducible to quadric trinomial solved example 1. factorise. solution : let and and Resubstituting the values of a and b we get

14. Logylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Std-9 th sub -Algebra Topic-algebraic expression Std-9 th sub -Algebra H) Factors of an expression of the form SOLVED EXAMPLE

15. Logylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Std-9 th sub -Algebra Topic-algebraic expression Std-9 th sub -Algebra

16. Logylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Std-9 th sub -Algebra Topic-algebraic expression Std-9 th sub -Algebra Exercise 3.5 Degree of a polynomial in one variable In case of a polynomial in one variable the highest power of the variable in the ppolynomial is called the degree of the polynomial. Degree of a polynomial in more than one variable In the case of a polynomial in more than one variable, the sum of the powers of the variables in each term is taken up and the highest sum so obtained is the degree of the polynomial. Standard form of an polynomial If the tems of a polynomial p(x) are either in ascending or descending powers of x,then such a form is called standard from of the polynomial.

17. Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Std-9 th sub -Algebra Topic-algebraic expression Std-9 th sub -Algebra 3.4 Operation on polynomials Addition,subtaction,multiplication, division Solved example 1.Simplyfy : solution :

18. Logylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Std-9 th sub -Algebra Topic-algebraic expression Std-9 th sub -Algebra Dividend =Divisor* Quotient + Reminder. Synthetic Division p(y) = 3y2+ 5y -7 q(y) = y+1 is divisor 3y2 +5y – 7 = ( 3, 5,-7) -1 35-7 -3-2 32-9 Remainder = -9, Quotient = ( 3,2) = 3y+2

19. Logylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Std-9 th sub -Algebra Topic-algebraic expression Std-9 th Sub-ALGEBRA 3.5 Value Of The Polynomial zeroes of the polynomial This subunit is newly introduced in this chapter If p(x) is a polynomial and ais a real number such that p(a) = 0 then a is said to be zero of the polynomial p(x) Or a is said to be zero of the polynomial p(x) if p(a)=o where a is a real number Ex : Find the zeroes of the polynomial x2-4 Groups of students are formed and each group is asked individually find p(a) where a = 0,1.-1, 2,- 2, 4.

20. Logylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Std-9 th sub -Algebra Topic-algebraic expression Std-9 th Sub- algebra 3.6 Reminder Theorem 1. find the remainder by using reminder theorem when the polynomial is divided by x-1. Solution : divisor is x-1. Ó. Put x = 1 in p (x). Ó. By reminder theorem remainder = p(1) =1-3(1)+1+1 = 1-3+1+1 = 0. ̇.reminder =0

21. Logylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Std-9 th sub -Algebra Topic-algebraic expression