Page 137 - ICSE Math 8

12 Fundamental Operations on

Algebraic Expressions

Key Concepts

• Algebraic Expression • Multiplication of Algebraic Expression
• Polynomial in One Variable • Division of Algebraic Expression
• Polynomial in Two or More Variables • Simplification of Algebraic Expression
• Addition and Subtraction of Algebraic Expressions

You are familiar with algebraic expressions and the operations of addition and subtraction on them. In this
chapter, we will extend our study to multiplication and division of algebraic expressions.
Before moving further, let us revise some basic concepts of algebra learnt in the previous classes.

Constant and Variable

A symbol having a fixed value is known as a constant and a symbol which can take different values as per the
1
requirement is known as a variable. For example, 2, –9 and 13 are constants, and letters like x, y, z, a and b
5
are variables. Variables are also known as literals or literal numbers.

Points to remember

• A combination of two or more constants is a constant.
• A combination of two or more variables is a variable.
• A combination of one or more constants and variables is a variable.

Term
A term can be a constant or a variable or a combination of both connected by multiplication or division.
3x 2
2
For example, 7x, –4y and are terms. If a term does not contain a variable, then it is known as a constant
7y
term. In a term, the constant part is known as the numerical factor and the variables are known as literal
factors.
For example, in –7xy, –7 is the numerical factor, and x, y and xy are literal factors. There are two types of
terms. They are like terms and unlike terms.

Like terms

The terms having the same literal factors are known as like terms. However,
they may or may not have the same numerical factor. For example, Try These
x x
(a) 15ab and 42ab (b) 10 and 17 1. Identify the pair of like terms.
y
y
2
2
(a) –18xy z, 24y xz
2
2
Unlike terms (b) 6xyz , –10x yz
2 2
2 2
(c) 15a b c, 9a c b
The terms with different literal factors are known as unlike terms. For example, 2. Find the coefficient of:
2 2
2
3
3
2
(a) 8a x and 8b y (b) 5ab and 5a b (a) –5xy in –5x y z
2
(b) yz in – yz 2
3
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