KENDRIYA VIDYALAYABOLPUR

MATHS POWER POINT PRESENTATION

Prepared by : Srijoti Mukherjee

TOPIC:

ALGEBRAIC EXPRESSIONS AND

IDENTIES

Some terms related to algebraic expression

i} ALGEBRAIC EXPRESSION: A combination of constants

and variables connected by the signs of fundamental

operations of addition, subtraction, multiplication or

division is called an algebraic expression.

Expression

coefficient of x 4x+6 constant

variable

ii} CONSTANT : It has a fixed value.Examples: 1,2,-4,-78 etc..

iii} VARIABLE: It can take various values. Its value is not fixed. We use alphabetical letters to denote variables.

Examples: x,y,a,b,c,z etc..iv} VALUE OF ANY EXPRESSION: suppose the expression is: 4x-2 at

x=3, 4x-2 ,x=3 =4X3-2 =12-2 = 10

TYPES OF ALGEBRAIC EXPRESSIONS:i} MONOMIALS: An algebraic expression is called

a monomial, if there is only one term in the

expression. Examples: x, 3z, 4y, 76x etc..ii} BINOMIALS: An expression containing only

two terms is called a binomial. Examples: x+y, y-5x, 3y*5z etc..iii} TRINOMIALS: An expression containing only

three terms is called a trinomial.

iv} POLYNOMIALS: Polynomials are algebraic

expressions having variables with non-negative

integral indices only. A polynomial may contains any

number of terms, one or more than one.

Examples: p +q +r +s, 8xy, 5x + 3y + 7z etc..

Note: Every polynomial is an algebraic

expression but every algebraic expression is not a

polynomial.

v} LIKE TERMS: Terms having same variables with

same exponents are called like terms. We can add or

subtract the coefficients of like terms only.

Example: 7x,4x,-15x are like terms.vi} UNLIKE TERMS: Terms having same

variables with different exponents or different

variables with same or different exponents are called unlike

terms.Example: 5x and 6y are unlike terms.

ADDITION AND SUBTRACTION *Algebraic expressions are added or

subtracted by adding or subtracting like terms of the

expressions. ADDITION: Add 42x+12y and 12xy+3x-8y 42x+ 12y+ 12xy+ 3x- 8y = 42x+3x +12y -8y + 12xy = 45x + 4y + 12xy (ans). SUBTRACTION: Subtract 9x -10 from 4x+5. 4x+5 – 9x -10 = 4x-9x + 5-10 = -5x – 5 (ans).

MULTIPLICATIONProduct of coefficients =coefficient of

first polynomial X coefficient of second polynomial.Product of algebraic factor =algebraic

factor of first polynomial X algebraic factor of second polynomial.

MULTIPLICATION: i} 5x (7y+6z) = 5x X 7y + 5x

X 6z = 35xy + 30xz

(ans). ii} (5x-6y) (4w+2z) =

5x(4w+2z) – 6y(4w+2z) = 5xX 4w+5x X 2z –

6y X 4w+ (-6y) X 2z = 20xw+10xz-

24yw – 12yz (ans).

CONCEPTS OF EQUATIONS AND IDENTITIES Algebric expression when equated

to some constant or other expression, gives rise to an equation.

OR, As the name suggests, an expression

with an equality sign, is commonly termed as equation.

An equality which is true for every value of the variable or variables is called an identity.

SOME STANDARD IDENTITIES:

WISHING THANKS TO: My Maths Teacher, math

books, internet and Wikipedia .