algebraic expressions and identities

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this my ppt on algebraic expressions and identities class 8 done by me venkat raja

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Algebraic expressions and identities:

Algebraic expressions and identities done by Venkat raja Class viii

What are expressions:

What are expressions A number or a combination of number Connected by the symbols of operation is called an algebraic expressions Equations are formed from variables and constants

Terms and factors:

Terms and factors Various parts of algebraic expressions which are separated by signs + or – are called the terms of the expressions. Each term is an algebraic expression is a product of one or more numbers know as the factor of that term

LIKE TERMS AND UNLIKE TERMS:

LIKE TERMS AND UNLIKE TERMS EXAMPLE 3X AND 7X LIKE TERM 6W AND 6Y UNLIKE TERMS 8Y ,2Y AND 3Y LIKE TERMS 5,85 AND 100 LIKE TERMS 4X AND 4XY UNLIKE TERMS 5X AND 8X UNLIKE TERMS THE TERMS HAVING THE SAME LITERAL FACTORS ARE CALLED LIKE TERM OTHER WISE THEY ARE CALLED UNLIKE TERMS

COEFFICENT:

COEFFICENT IN ATERM OF AN ALGEBRAIC EXPRESSIONS ANY OF THE FACTOR WITH OUT SIGN OF THE TERM IS CALLED COEFFICIENT OF THE PRODUCT OF THE FACTOR 4X – 5 = 7 CONSTANTS= 4 , 5 , 2 VARIABLE = X

MONOMIALS:

MONOMIALS THE EXPRESSION WHICH CONTAINS ONLY ONE TERM IS CALLED MONOIAL EXAMPLE 3XY , 6XY 2

BINOMIALS:

BINOMIALS THE EXPRESSIONS THAT CONTAINS TWO TERMS IS CALLED BINOMIALS EXAMPLE 4XY+ 5XY

TRINOMIALS:

TRINOMIALS THE EXPRESSION CONTAINING 3 TERMS IS CALLED TRINOMIALS EXAMPLE 4XY + 9XY – 8XY 2

POLYNOMIALS:

POLYNOMIALS THE EXPRESSION CONTAINIG ONE OR MORE TERMS ARE CALLED POLYNOMIALS EXAMPLE 4XY – 4 – 5XY + 89 + 7XY

ADDITION OF ALGEBRAIC EXPRESSIONS:

ADDITION OF ALGEBRAIC EXPRESSIONS ADD THE FOLLOWING [3X 3 + 2X - 5] + [ 2X 3 + X +9] = 3X 3 + 2X 3 + 2X + X -5 +9 = 5X 3 + 3X + 4 THIS HOW WE ADD ALGEBRAIC EXPRESSIONS

Subtraction of algebraic expressions:

Subtraction of algebraic expressions – (4x3 + x2 + x + 6) – (2x3 - 4x2 + 3x + 5) = 4x3 + x2 + x + 6 - 2x3 + 4x2 - 3x – 5 = 4x3 - 2x3 + x2 + 4x2 + x -3x + 6 – 5 = 2x3 + 5x2 – 2x + 1 ……………….THIS IS HOW WE SUBTRACT ALGEBRAIC EXPRESSIONS.

MULTIPLICATION OF TWO MONOMIALS :

MULTIPLICATION OF TWO MONOMIALS EX. MULTIPLY : (3ab) x (5b) = (3 x 5) x (ab x b) = 3 x 5 x [a x (b x b)] = 15 x [a x b2] = 15 x ab2 = 15ab2 ……………….THIS IS HOW WE MULTIPLY TWO MONOMIALS.

MULTIPLICATION OF A MONOMIAL AND A BINOMIAL :

MULTIPLICATION OF A MONOMIAL AND A BINOMIAL MULTIPLY : 2x by (3x + 5y) = (2x x 3x) + (2x x 5y) = 6x2 + 10xy ……………….THIS IS HOW WE MULTIPLY A MONOMIAL BY A BINOMIAL .

MULTIPLICATION OF A MoNOMIAL BY A TRINOMIAL  :

MULTIPLICATION OF A MoNOMIAL BY A TRINOMIAL  EX. MULTIPLY : 3p x (4p2 + 5p + 7) = (3p x 3p2) + (3p x 5p) + (3p x 7) = 9p3 + 15p2 + 21p ……………….THIS IS HOW WE MULTIPLY A MONOMIAL BY A TRINOMIAL .

MULTIPLICATION OF TWO BINOMIALS :

MULTIPLICATION OF TWO BINOMIALS EX: MULTIPLY – (3x + 2y) and (5x + 3y) = (3x + 2y) x (5x + 3y) = 3x x (5x + 3y) + 2y x (5x + 3y) = (3x x 5x + 3x x 3y) + (2y x 5x + 2y x 3y) = 15x2 + 9xy + 10xy + 6y2 = 15x2 + 19xy + 6y2 ……………….THIS IS HOW WE MULTIPLY A MONOMIAL BY A TRINOMIAL.

MULTIPLICATION OF A BINOMIAL BY A TRINOMIAL  :

MULTIPLICATION OF A BINOMIAL BY A TRINOMIAL  EX: MULTIPLY – (a + b) (2a – 3b + c) - (2a - 3b + c) = a (2a – 3b + c) + b (2a – 3b + c) = 2a2 – 3ab + ac + 2ab – 3b2 + bc = 2a2 – ab + ac – 3b2 + bc ……………….THIS IS HOW WE MULTIPLY A MONOMIAL BY A TRINOMIAL.

WHAT IS AN IDENTITY? :

WHAT IS AN IDENTITY? AN IDENTITY IS AN EQUALITY WHICH IS TRUE FOR ALL VALUES OF THE VARIABLE

STANDARD IDENTITIES :

STANDARD IDENTITIES

IDENTITIY 1:

IDENTITIY 1 (a + b)2 = a2 + 2ab + b2 or, (a + b)2 = a2 + b2 + 2ab i.e., Square of the sum of two terms = (Square of the first term) + (Square of the second term) + 2 x (First term) x (Second term) Proof: (a + b)2 = (a + b)(a + b) =(a + b)2 = a (a + b) + b (a + b) =(a + b)2 = a2 + ab + ba + b2 =(a + b)2 = a2 + ab + ab + b2 =(a + b)2 = a2 + 2ab + b2 =(a + b)2 = a2 + b2 + 2ab

IDENTITIY 2:

IDENTITIY 2 (a - b)2 = a2 - 2ab + b2 or, (a - b)2 = a2 + b2 - 2ab i.e., Square of the difference of two terms = (Square of the first term) + (Square of the second term) + 2 x (First term) x (Second term) Proof: (a - b)2 = (a - b)(a - b) =(a - b)2 = a (a - b) - b (a - b) =(a - b)2 = a2 - ab - ba + b2 =(a - b)2 = a2 - ab - ab + b2 =(a - b)2 = a2 - 2ab + b2 =(a - b)2 = a2 + b2 - 2ab

IDENTITIY 3:

IDENTITIY 3 (a + b)(a - c) = a2 – b2 i.e., (First term + Second term) (First term - Second term) = (First term)2 – (Second term)2 Proof: (a + b)(a - b) = a (a - b) + b (a - b) =(a + b)(a - b) = a2 - ab + ba – b2 =(a + b)(a – b) = a2 – ab + ab – b2 =(a + b)(a – b) = a2 – b2

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