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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 > Coefficients

Coefficients

We have learnt how to write a term as a of factors. One of these factors may be numerical and the others algebraic (i.e., they contain variables).

The numerical factor is said to be the numerical coefficient or simply the coefficient of the term.

It is also said to be the coefficient of the rest of the term (which is obviously the product of algebraic factors of the term).

Thus, in 5xy, 5 is the coefficient of the term.

It is also the coefficient of xy. In the term 10xyz, is the coefficient of xyz, in the term −7x2y2 is the coefficient of x2y2.

What are the terms in the following expressions? Show how the terms are formed. Draw a tree diagram for each expression.

(i) 8y + 3x2y

Instruction

8y + 3x2y The terms in the expression are
8y and 3x2
8y + 3x2y is obtained by the product of 8 and y with the product of 3 x and x.

(ii) 7mn-4

Terms of 7mn-4 are 7mn and -4.
The term 7mn formed by first variables m and n to get m x n = mn.
Then mn by constant 7 to get 7 x mn.
The term is a constant.

(iii) 2x2y

2x2y has only one term, that is the expression itself.
The expression is formed by 4 terms 2, x, x and y.

When the coefficient of a term is +1, it is usually omitted.

For example: 1x is written as x; 1x2, 1y2 is written as , respectively and so on.

Similarly, the coefficient −1 is indicated only by the minus sign. Thus −1x is written as −x; −1x2 , −1y2 is written as , and so on.

Sometimes, the word ‘coefficient’ is used in a more general way.

Thus, we say that in the term 5xy, is the coefficient of xy, is the coefficient of 5y and is the coefficient of 5x

In 10xy2 is the coefficient of , x is the coefficient of 10y2 and is the coefficient of 10x.

Thus, in this more general way, a coefficient may be either a numerical factor or an algebraic factor or a product of two or more factors. It is said to be the coefficient of the product of the remaining factors.

Identify the coefficientsof the terms of following expressions: 4x – 3y, a + b + 5, 2y + 5, 2xy

(i)4x – 3y

Instruction

4x-3y has two terms 4x and -3y.
The coefficient of x is and the coefficient of y is .

(ii)a + b + 5

a+b+5 has 3 terms a,b and a constant that is 5.
The coefficient of a is and b is also . Constant terms have coefficient.

(iii)2y + 5

2y+5 has two terms 2y and 5 which is constant.
The coefficient of y is . Constant terms have coefficient.

(iv)2xy

2xy has only one term
which is 2xy and the coefficient of xy is .

Identify, in the following expressions, terms which are not constants. Give their numerical coefficients.

xy + 4, 13 –y2, 13 – y + 5y2,4p2q - 3pq2 + 5

S. NoExpressionTerm (which is not a Constant)Numerical Coefficient
(i)xy + 4
(ii)13-y2
(iii)13 – y + 5y2– y + 5y2 and
(iv)4p2q -3pq2+54p2q -3pq2 and

(a) What are the coefficients of x in the following expressions? 4x – 3y, 8 – x + y,y2x-y,2z – 5xz

Solution :

S. NoExpressionTerm with factor xCoefficient of x
(i)4x – 3y
(ii)8 – x + y
(iii)y2x-y
(iv)2z – 5xz

(b) What are the coefficients of y in the following expressions? 4x – 3y, 8 + yz, yz2 + 5, my + m

Solution :

S. No.. ExpressionTerm with factor yCoefficient of y
(i)4x – 3y
(ii)8 + yz
(iii)yz2+ 5
(iv)my + m