Page 90 - Start Up Mathematics_8 (Non CCE)

5 Algebraic Expressions and Identities:

Part I

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.
Algebraic expression: An algebraic expression is a phrase with one or more algebraic terms. It can include
variables and constants connected by fundamental operations i.e., +, –, ¥ and ÷. For example, the phrase
2
4
3x + 2y + 7xy + 5 and 7x – 8 x are algebraic expressions.
Terms: In an algebraic expression, terms are the elements separated by ‘+’ or ‘–’ sign. They may consist of
2
variables and coefficients or constants. For example, in the algebraic expression 3x + 2y + 7xy + 5 the terms
2
are 3x , 2y, 7xy and 5.
Constant: Constants are the terms in the algebraic expressions that contain only numbers. Their value never
2
changes. For example, in the algebraic expression 7x + 3xy + 8, the constant term is 8.
Variable: In the algebraic expressions, letters represent variables. Variables are also called literals. For example,
2
in the algebraic expression 3x + 2y + 7xy + 5, x and y are the variables. Variables can take different values.
Coefficient: Coefficients are the number part of the terms with variables. For example, in the algebraic expression
2
2
3x + 2y + 7xy + 5, coefficient of 3x is 3, coefficient of 2y is 2, and coefficient of 7xy is 7.
Polynomial: It is an algebraic expression in which the exponents of the variables is a non-negative integer.
3
For example, 7x + x is a polynomial while 7x + 1 is not.
2
x 2
Monomial: An algebraic expression containing only one term where the variables have non-negative integral
1
3 2
2
2 34
3
powers is called a monomial. For example, 7x y, –4x y z, ab, - 3 ab c 7 , are all monomials.
2 4
Binomial: An algebraic expression containing two terms where the variables have non-negative integral
2
3 3
2
powers is called a binomial. For example, 4x – 3y, 3a b + 2ab , 2xy – 3, 4x y – 7xy are all binomials.
Two monomials containing unlike terms, when added give a binomial.
Trinomial: An algebraic expression containing three terms where the variables have non-negative integral
2
2
3
powers is called a trinomial. For example, 2a + 3b – c, 4x – 5x + 6, 7xy + 8x – 2y are all trinomials.
Factors: Each term in an algebraic expression is a product of one or more number(s) and/or literal(s) which
are the factors of that term. A constant factor is called a numerical factor while a variable factor is known as
literal factor. For example, in 5x, 5 is the numerical factor and x is the literal factor.
Like and unlike terms: Like terms in an algebraic expression are terms with identical symbolic variable parts,
3 2
3 2
2
3 2
3 2
otherwise they are unlike terms. For example, in the algebraic expression 5x y – 7xy – 8x y , 5x y and –8x y
3 2
2
3 2
2
are like terms, whereas, 5x y and –7xy or –8x y and –7xy are unlike terms.
EXERCISE 5.1
1. Identify the terms and their coefficients in the following algebraic expressions:
2
2
2
3
2
(a) 12 + x + y – zx (b) 4x y – 7x + 3y 4 (c) 1 a – 3a b (d) 9.2x – 4.1yz + 2x yz 2
2