.png)
Chapter –12
Algebraic Expressions
Algebraic expressions are formed from variables and constants. We use the operations of addition, subtraction, multiplication and division on the variables and constants to form expressions.
For example, the expression 4xy + 7 is formed from the variables x and y and constants 4 and 7.
The constant 4 and the variables x and y are multiplied to give the product 4xy and the constant 7 is added to this product togive the expression.
Variable: Symbols which are used to represent or replace numbers.
They are denoted as x, y, z, a, b, c…… and can take different numerical values.
We generally use small letters torepresent variables.
Constant: A symbol having a fixed numerical value. Example: 2,-10, etc.
Expressions are madeup of terms.
Terms are added to make an expression.
For example, the addition of the terms 4xy and 7 gives
the expression 4xy + 7.
A term is a product of factors.
The term 4xy in the expression 4xy + 7 is a product of factors x, y and 4.
Factors containing variables are said to be algebraic factors.
The coefficient is the numerical factor in the term.
Sometimes anyone factor in a term is called thecoefficient of theremaining part ofthe term.
Any expression with one or more terms is called a polynomial.
Specifically a oneterm expression is called a monomial.
A two-term expression is called a binomial.
A three-term expression is called a trinomial.
Terms whichhave the samealgebraic factors are like terms.
Terms which have different algebraic factors are unlike terms.
Thus, terms 4xy and – 3xy are like terms; butterms 4xy and – 3x are not like terms.
The sum (or difference) of two like terms is a like term with coefficient equal to the sum (or difference) of thecoefficients of thetwo like terms.
Thus, 8xy – 3xy = (8 – 3 )xy, i.e., 5xy.
When we add two algebraic expressions, the like terms are added as given above; the unlike terms areleft as they are.
Thus, the sumof and 5.
In x^9 , 9 is called the index or exponent and x is called the base.
In a^5 , the index or exponent is 5 and the baseis a.
A symbol having a fixed numerical value is called a constant.
A symbol which takes various numerical values is called a variable.
A combination of constants and variables connected by the signs of fundamental operations of addition, subtraction, multiplication anddivision is called an algebraic expression.
Various parts of an algebraic expression which are separated bythe signs of‘+ ' or ' −' arecalled the terms of the expression.
An algebraic expression iscalled a monomial, a binomial, a trinomial, aquadrinomial according as it contains one term,two terms, three terms andfour terms respectively.
Each term in analgebraic expression is a product of one or more number(s) and/or literal number(s). These number(s) and or literal number(s) are knownas the factors of that term.
A term of theexpression having no literal factor is called aconstant term.
In a term ofan algebraic expression any of thefactors with the signof the termis called the coefficient of theproduct of thefactors.
The terms having the sameliteral factors arecalled like orsimilar terms.
The terms not having sameliteral factors are called unlike or dissimilar terms.
The sum or difference of several liketerms is another like term whose coefficient is the sumor difference of those liketerms.
In adding or subtracting algebraic expressions, wecollect different groups of like termsand find the sum or difference of liketerms in eachgroup.
To subtract an expression from another, we change the sign (from + ' to’ − ' and from ‘−' to + )of each termof the expression to be subtracted and then addthe two expressions.
The letters which areused to represent numbers are called literal numbers or literals.
The literal numbers themselves as well asthe combinations ofliteral numbers andnumbers obey all the rules (and signs) of addition, subtraction, multiplication and division of numbers along withthe properties of these operations.
x´ y = xy, 5´ x = 5x, 1´ x = x, x´ 4 = 4x.
a´a´....´12times= a^12, y ´ y ´....... ´15times =y^15.
In situations such as solving an equation and using a formula, we have to find the value of an expression.
The value of the expression depends on the value of the variable from which the expression is formed.
Thus, the value of 7x – 3 for x = 5 is 32, since 7(5) –3 = 35 – 3= 32.
Rules and formulas in mathematics are written in a concise and general form using algebraic expressions:
Thus, the area of rectangle = lb, where l is the length and b is thebreadth of therectangle.
The general (nth) term of a number pattern (or a sequence) is an expression in n.
Thus, the nth term of the number pattern 11, 21, 31,41, . . . is (10n + 1). 2x + 3 is are leftas they are.
; the like terms 5x and 2x add to 7x; the unlike terms and 3.
Comentarios