Algebraic expression<br />A Combination of constants and variables connected by the signs of fundamental operations of addition,subtraction, division and multiplication is called an algebraic expression. <br />Terms <br />Various parts of an algebraic expression which are seprated by the signs+ or – are called the ‘terms’ of the expression.<br />Illustration-3y+4x is an algebraic expressions having 3y and 4x as terms<br />
Types of Algebraic expressions<br />Monomial- an algebraic expression containing only one term <br />Example-3x , 4z, 2y ,5t are monomials.<br />Binomial-An algebraic expression containing two terms.<br />Example-3y+5x , 4z-6y , 2x+6x are binomials.<br />Trinomial-An algebraic expression containing three terms.<br />Example-3x+4z-2w , 5y+4z-3x, 4z-1y+10x are trinomials.<br />Quadrinomial-An algebraic expression containing four terms.<br />Example-3y+x+6y-7x , 4z+5z-6x+10x are quadrinomials.<br />
Polynomial<br />An algebraic expression two or more terms is called a polynomial.<br />Factors<br />Each term in an algebraic expression is a product of one or more number[s] and/ or literal number(s).These number(s) are known as the factors of that term. <br /><ul><li>Illustration- The monomial 7x is the product of the number 7 and literal x. So 7 and x are the factors of monomial 7x .
In the term -4xyz , the numerical factor is -4 and x, y , z are literal factors.
In he binomial expression xy+3 , the term xy has 1 as its numerical factor while x and y are literal factors. The term 3 has only numerical factor. It has no literal factor. </li></li></ul><li>Constant term<br />A Term of the expression having no literal factor is called a constant term<br />Illustration-In the binomial expression 5x + 7 ,the constant term is 7. <br />COEFFICIENT <br />In a term of an algebraic expression, any of the factors with the sign of the term is called the coefficient of the product of the other factors.<br /><ul><li>Illustration-In the monomial 3xy,the coefficient of xy is 3,the coefficient of x is 3y, the coefficient of y is 3x.
Consider the term -8xy in the binomial -8xy+7.The coefficient of x is the term -8xy is -8y the coefficient of y is -8x and the coefficient of xy is -8</li></li></ul><li>Like Terms<br />The terms having the same literal factors are called like or similar terms<br />Unlike terms<br />The terms not having same literal factors are called unlike or dissimilar terms.<br />Illustration- In the algebraic expression 5xy+8xy -3yz-9yc, we have 5xy and 8xyas like terms, whereas -3yz and -9yc are unlike terms.<br />In the expression 16x,16y we have 16x and 16y as unlike terms because the literal factors x and y are not same.<br />
Addition of negative like terms.<br />Step1-Obtain all like terms.<br />Step2-Obtain the sum of the numerical coefficients (without the negative sign) of all like terms.<br />Step3-Write an expression as a product of the number obtained is step2, with all the literal coefficients preceded by a minus sign.<br />Step4-The expression obtained in step3 is the required sum.<br />Add -7xy,-3xy,-9xy<br />The sum of the numerical coefficients(without the negative sign) is<br />7+3+9=19 <br />Hence -7x,-3xy,-9xy=-19xy<br />
Operations On Algebraic Expression.<br />Addition of positive terms<br />Procedure- <br />Obtain all like terms.<br />Find the sum of the numerical coefficients of all like terms.<br />Write the required sum as a like term whose numerical coefficients is the numerical obtained in step 2 and literal factors of the given like terms.<br />Illustration-Add 4xy ,12xy and 3xy<br />Solution- The sum of the numerical coefficients of the given like terms is 4+12+3=19.<br />Thus the sum of the given like terms is another like term whose numerical coefficient is 19.<br />Hence,4xy+12xy+3xy=19xy.<br />Aliter-the sum of the given like terms can also be obtained by using the distributive property of multiplication over addition as discussed below-<br />4xy+12xy+3xy=(4+12+3)xy=19xy<br />
Addition of +ive and –ive like terms<br />Step1-Collect all +ive like terms and find their sum.<br />Step2-Collect all the -ive like terms and find their sum.<br />Step3-Obtain the numerical coefficients(without -ive sign) of like terms obtained in steps1 and 2.<br />Step4-Subtract the numerical coefficient in step2 from the numerical coefficient in steop1.Write the answer as a product of this number and all the literal coefficients.<br />Add 4xy,8xy,-2xy<br />4xy+8xy- 2xy<br />(4xy+8xy)-2xy (Collecting +ive and –ive like terms together) 12xy-2xy=10xy<br />
Addition of algebraic expression with an unlike terms like<br />In adding algebraic expression containing like and unlike terms we collect different groups of like terms and find the sum of like terms in each groups by the methods discussed below-<br />1)Horizontal method 2)Column method<br />(7x+4)+(3x-1) 7x+4 <br />=(7x+3x)+(4-1) +3x-1 <br />=10x+3 =10x+3<br />
Subtraction of algebraic expression<br />To subtract an algebraic expression from another we should change signs(from + to – or from – to+)of all the expression which is to be subtracted and then the two expressions are added.<br />Subtract 5x from 9x<br />9x-5x=4x<br />Subtract x+y from 5x-3y<br />(5x-3y)-(x+y)<br />5x-3y-x-y<br />(5x-x)-3y-y<br />4x-4y<br />