PPT on algebraic expressions and identities
- 1. NAME : Talib CLASS : XII “A” ROLL : 01 SUBJECT : MATHS KENDRIYA VIDAYALAYA, Masjid Moth, Sec-3, Sadiq Nagar, New Delhi-110049
- 2. We have already become familiar with what algebraic expressions are. Examples of expressions are : x + 3, 2y – 5, 3x2, 4xy + 7 etc. You can form many more expressions. As you know expressions are formed from variables and constants. The expression 2y – 5 is formed from the variable y and constants 2 and 5. the expression 4xy + 7 is formed from variable x and y and constants 4 and 7. We know that, the value of y in the expression, 2y – 5, may be anything. It can be 2, 5, -3, 0, 5/2, -7/3 etc.; actually countless different values. The value o an expression changes with the value chosen for the variables it contains. Thus as y takes on different values, the value of 2y – 5 goes on changing. When y = 2, 2y – 5 = 2(2) – 5 = -1; when y = 0, 2y – 5 = 2 x 0 – 5 = -5, etc. Find the value of the expression 2y – 5 for the other given value of y.
- 3. Take the expression 4x + 5. this expression is made up of two terms, 4 x and 5. Terms are added to form expression. Terms themselves can be formed as the product of factors. The term 4x is the product of its factors 4 and x. the term 5 is made up of just one factor, i.e., 5. The expression 7xy – 5x has two terms 7xy and - 5x. The term 7xy is a product of factors 7, x and y. the numerical factor of a term is called its numerical coefficient or simply coefficient. The coefficient in the term 7xy is 7 and the coefficient in the term – 5x is -5.
- 4. Expression that contains only one term is called a monomial. Expression that contains two terms is called a binomial. An expression containing three terms is a trinomial and so on. In general, an expression containing, one or more terms with non-zero coefficient is called a polynomial. A polynomial may contain any number of terms, one or more than one. Examples of monomials : 4x2, 3xy Examples of binomials : a + b, 4l + 5m Examples of trinomials : a + b – c, 2x + 3y – 5 Examples of polynomials: a + b + c + d, 3xy
- 5. We have also learnt how to add, subtract & multiply algebraic expression. For example : Add. : 7x2 – 4x + 5 + 9x – 10 7x2 + 5x – 5 Subtract : 7x2 – 4xy +8y2 + 5x – 3y 5x2 - 4y2 + 6y – 3 (-) (+) (-) (+) 2x2 – 4xy + 12y2 + 5x – 9y + 3 Multiply : 2x x 5y x 7z = (2x x 5y) x 7z = 70xyz
- 6. We shall find that for any value of a, LHS=RHS. Such an equality, true for every value of the variable in it, is called an identity. Thus, (a + 1) (a + 2) = a2 + 3a + 2 is an identity. Standard Identity: (a + b)2 = a2 + 2ab + b2 (a – b)2 = a2 – 2ab + b2 (a + b) (a – b) = a2 – b2 (x +a) (x +b) = x2 + (a +b) x + ab
- 7. 1. (2x + 3y)2 (a + b)2 = a2 + 2ab + b2 (2x + 3y)2 = (2x)2 + 2(2x) (3y) + (3y)2 = 4x2 + 12xy + 9y2 2. (4p – 3q)2 = (4p)2 – 2(4p) (3q) + (3q)2 = 16p2 – 24pq + 9q2 3. (3/2m + 2/3n) (3/2m – 2/3n) = (3/2m)2 – (2/3n)2 = 9/4m2 – 4/9n2 4. 501 x 502 = (500 + 1) x (500 + 2) = 5002 + (1 + 2) x 500 + 1 x 2 = 250000 + 1500 + 2 = 251502