Rayat Shikshan Sanstha Karmaveer Vidyaprabodhini Madhya vibhag Satara

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

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

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

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

Rayat Shikshan Sanstha, Karmaveer Vidyaprabodhini, Madhya vibhag, Satara. Std-9 th sub -Algebra 3. 1 OPRATIONS ON ALGEBRAIC EXPRESSIONS: Addition and subtraction of algebraic expressions. Logylogyat Terms with same variables and having same powers are like terms. Solved examples: Add 2 a + 3 b-15 c and 4 a-7 b+8 c. 2 a+3 b-15 c 4 a-7 b+8 c 6 a-4 b-7 c sub -Algebra Topic - Algebraic Expression Std-9 th

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

Rayat Shikshan Sanstha, Karmaveer Vidyaprabodhini, Madhya vibhag, Satara. sub -Algebra Std-9 th 3. 2 Factorization of an algebraic expretion (a)By taking out the common factores: Factorise : 5 x+20 y Solution : 5 x+20 y=5(x+4 y) Logylogyat here 5 and (x+4 y)are the factores of 5 x +20 y. 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) Std-9 th sub -Algebra Topic-algebraic expression

Rayat Shikshan Sanstha, Karmaveer Vidyaprabodhini, Madhya vibhag, Satara. sub -Algebra Std-9 th c) Factorise of difference of two squares: Logylogyat Exercise 3. 2 factorise the following. 1. 4 x-8 y =4(x-2 y) Std-9 th sub -Algebra Topic-algebraic expression

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

Rayat Shikshan Sanstha, Karmaveer Vidyaprabodhini, Madhya vibhag, Satara. sub -Algebra Std-9 th Exercise 3. 3 Logylogyat Std-9 th sub -Algebra Topic-algebraic expression

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

Rayat Shikshan Sanstha, Karmaveer Vidyaprabodhini, Madhya vibhag, Satara. sub -Algebra Std-9 th Solution : Since 2*5=10 and 2+5=7 Logylogyat Exercise 3. 4 Factorise the folloving : 1. Std-9 th sub -Algebra Topic-algebraic expression

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

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

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

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

Rayat Shikshan Sanstha, Karmaveer Vidyaprabodhini, Madhya vibhag, Satara. sub -Algebra Std-9 th 3. 4 Operation on polynomials Addition , subtaction , multiplication , division Solved example 1. Simplyfy : solution : Std-9 th sub -Algebra Topic-algebraic expression

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

Rayat Shikshan Sanstha, Karmaveer Vidyaprabodhini, Madhya vibhag, Satara. Sub-ALGEBRA Std-9 th 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 Logylogyat 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 x 2 -4 Groups of students are formed and each group is asked individually find p(a) where a = 0, 1. -1, 2 , - 2 , 4. Std-9 th sub -Algebra Topic-algebraic expression

Rayat Shikshan Sanstha, Karmaveer Vidyaprabodhini, Madhya vibhag, Satara. Sub- algebra Std-9 th 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 Logylogyat = 1 -3+1+1 =0. . reminder =0 Std-9 th sub -Algebra Topic-algebraic expression

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