Page 75 - Maths Skills - 8

Algebraic Expressions and Identities 73

INTRODUCTION
We have been introduced to algebraic expressions in our previous class. In this chapter, we shall learn about
addition, subtraction and multiplication of algebraic expressions. We shall also learn about algebraic identities.

TERMS IN ALGEBRA

Algebraic Expressions Smart Tip
An algebraic expression is a combination of constants and variables, connected by any or all of the four fundamental
operations (+, –, ×, ÷).
The different parts of the expression separated by the sign ‘+’ or ‘–’ are called the terms of the expression.
For example, the expression 4 + 7xy – 6x y has 3 terms, namely, 4, 7xy and – 6x y .
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Monomials
An algebraic expression containing one term is called a monomial.

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For example, – 19, a , 3x y , − 8 x yz , etc. are monomials.
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Binomials
An algebraic expression containing two terms is called a binomial. Fact-o-meter
For example, (a + b ), (7x + 9y), (3a b + 8), etc. are binomials. Expression 2a + 5a is
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not a binomial, because
Trinomials 2a + 5a = 7a, which is a
An algebraic expression containing three terms is called a trinomial. monomial.
For example, (2a + b – c), (x – y + 4xy), etc. are trinomials.
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Polynomial Fact-o-meter
An algebraic expression that contains two or more terms is
called a polynomial. A polynomial can have no literal or
For example, – 3xy + 2xy + 5x + 7 is a polynomial. variable in the denominator, e.g., 8
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Degree of a Polynomial is not a monomial, 7a + 5a is not a
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The highest power of the variable of a polynomial in one polynomial, 8xy – 3x y + x y is not
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variable is called the degree of polynomial. 9
In case of polynomial in more than one variable, the degree is a polynomial, etc.
the highest sum of the exponents of variables among each them.
For example, (i) Degree of 9x is 6 (ii) Degree of –4x y is 5 (i.e. 3 + 2)
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(iii) Degree of polynomial 5xy – 6x y + 3x y – 7 is 6 (i.e. 1 + 5)
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Like and Unlike Terms
The terms having same literal factors are called like terms or similar terms, otherwise while those having different
literal factors are called unlike terms.
For example, the terms 3ab , 5ab and – 8b a are like terms whereas 2a b , – 3ab and 7a b are unlike terms.
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ADDITION AND SUBTRACTION OF ALGEBRAIC EXPRESSIONS
To add or subtract two or more algebraic expressions, first we collect the like terms and find the sum or difference
of the constant coefficients of these terms.