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Chapter 10: Algebraic Expressions

    Introduction

    How are Expressions Formed

    Terms of an Expression

    Factors of a term

    Coefficients

    Like and Unlike Terms

    Monomials, Binomials, Trinomials and Polynomials

    Finding the Value of an Expression

    Exercise 10.1

    Exercise 10.2

    What Have We Discussed ?

    Extra Curriculum Support

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Chapter 10: Algebraic Expressions > Factors of a term

Factors of a term

We saw above that the expression 4x2−3xy

Consists of two terms 4x2 and −3xy.

The term 4x2 is a product of , x and x

We say that 4, x and x are the factors of the term 4x2 A term is a of its factors.

The term −3xy is a product of the factors , and y.

We can represent the terms and factors of the terms of an expression conveniently and elegantly by a tree diagram. The tree for the expression 4x2–3xy, is as shown in the adjacent figure.

Note: In the tree diagram, we have used dotted lines for factors and continuous lines for terms. This is to avoid mixing them.

Let us draw a tree diagram for the expression 5xy + 10.

The factors are such that they cannot be further factorised. Thus we do not write 5xy as 5 × xy, because xy can be further factorised.

Similarly, if x3 were a term, it would be written as x × x × x and not x2 × x. Also, remember that is not taken as a separate factor.