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+ 4 % 1 ¼ 3 ÷ ¾

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Chapter6 6 ½ –

Algebraic Expressions

Introduction (i) Like terms: The terms having the same
literal (variable) with same exponents are
A combination of numerical and literal
numbers connected by the symbols +, -, ´ and ¸ called Like terms.
1
is called an al ge braic ex pres sion. We Example: 12x and -5x 4x and x 2
2
gen er ally drop the sym bol ´ for mul ti pli ca tion 2
in volv ing a lit eral num ber. For ex am ple, 2abc, (ii) Unlike terms: The terms having the same
2xy + 5yz and 3a + b + c are all algebraic variable with different exponents or different
ex pres sions. A nu mer i cal num ber, a lit eral or a variable with same exponents are
com bi na tion of nu mer i cal and lit eral num bers called Unlike terms .
con nected with mul ti pli ca tion or di vi sion is
2
2
called a term. In 2xy + 5yz there are two terms, Example: 5x and 5y 2x and 3y
2
namely, 2xy and 5yz. The ex pres sion 2abc has 4x and 5x 3
only one term while 2a + b + c has three terms.
In the term 2a, the num ber 2 is the nu mer i cal Some more examples :
co ef fi cient. How ever, when we say co ef fi cient 1. In the algebraic expression 5x y + 7xy 2
2
of x in -6xyz, we mean the term -6yz. 2
- 3xy - 4yx
In this chapter we will extend our studies 2 2
Like terms 5x y and -4yx
about other arithmetic operations on algebraic 2
Unlike terms 7xy and -3xy
expressions. But before proceeding further let
2
2
us revise what we have learnt in our previous 2. In the algebraic expression a - 3 b +
2
2
classes. 7b - 9a + 6ab + 5
2
2
2
Con stant ® A quantity that has a fixed Like terms a and -9a , -3b and 7b 2
numerical value is called a constant, for Unlike terms 5xy and 6ab
7
ex am ple -2, 8, .
3 Poly no mial
Vari able ® A quantity which can take An algebraic expression in which the powers
var i ous nu mer i cal val ues is called a vari able. of variables are whole numbers is called a
Lit eral ® In al ge bra al pha bets such as a, b, c, polynomials.
x, y, z etc. are used to represent variable are For example: x + 5, x + 3 x - 4,
3
2
2
called lit er als.
2
2x - 7xy + 6y 2
Al ge braic Ex pres sions® An Al ge braic
3
2
2
ex pres sion is a com bi na tion of con stants and Here x + 5 and x + 3 x - 4 are a polynomial
lit er als con nected by signs of ba sic arith me tic in one variable x.
op er a tions . And 2x - 7xy + 6y 2 is a polynomial in two
2
2
2
2
2
For example: 3a b xy, 2 + 4y x - 3m n + 2 mn . variables
Like and Unlike Terms Degree of a polynomial
In this section we will discuss about like and Highest power of the variable in a polynomial
unlike terms in solving algebraic expressions. is called its degree.

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Mathematics In Focus - 8