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Chapter6 6 ½ –

Algebraic Expressions

Generation of Algebraic expressions For ex am ple : Find Con stants from fol low ing
In Class VI, we have read some basic concepts se ries of al ge braic num bers.
,
k
,
and definitions on algebra and algebraic 24x ac, 4 93s
expressions. In this chapter, we shall study Constants in the given series are :
some, more basic concepts on algebraic = 24, 1, 4, 93
expressions.
Powers of Literals
Literal Number
As you have studied earlier in topic
In Algebra, we many times use English
‘Exponents’ that:
alphabets like a x y z, , , to represent a variable. 8
So, we call all such English alphabets as 10 means 10 is base and 8 is called power or
Lit eral Num bers. exponent of number 10
In simple words, an Eng lish Al pha bet that is Similarly, in algebra:
5
used to rep re sent a vari able is called a Lit eral a means that a is variable and 5 is the power
Num ber. of variable ‘‘a’’
For ex am ple : Find out Lit eral num bers from This also means that variable (a) is multiplied
given al ge braic num bers five times by itself.
24x ac, 4 93s And algebraic number ‘ ’x has 1 as its power.
,
k
,
1
Or we can say that x = x
= Literal numbers = x a c k s.
,
,
,
,
This means that when a variable has 1 as its
Variables and Constants
power, its power is ignored and only variable is
The Word Vari able means something which written as such.
can change.
Also, power of variable is also similar to what
Many times, we experience some events/ you studied in various laws of exponents like :
situation whose values are different, like a m ´ a = a m n or
+
n
number of days in a month, height of persons, m n m n
-
a ¸ a = a or
length of roads, etc.
m
a m ´ b m = ( ab) etc.
In Algebra, to represent such values we attach
a symbols to them. Algebraic Expression
For ex am ple; length and breadth of a A combination of constants and variables
rect an gle is rep re sented as l and b re spec tively. connected by the signs of fundamental
operations (+, - , ¸, ´) is called an algebraic
Here, l and b doesn't carry any particular value 2 2 2 2
+
,
and so they are called Vari ables. expression,i e x. .4 + y x + y , a - 2 ab b , etc.
If every term of an expression is a constant
The value of a Vari able is not fixed. Vari able
can have different values in different term then the expression is called a numerical
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sit u a tions. expression. i e. . -12 + 21 + 63 + etc.
2
In Algebra, Con stants are those numbers
which have fixed values and whose values Algebraic Terms
can't be changed or al tered. The parts of an algebraic expression separated
Therefore, we can say all Numbers or Integers by the operational signs “+” and “-” are called
,
are known as Con stants in al ge bra. its terms, i.e. in x + y x and y are its two terms.
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Mathematics In Focus - 7