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NCERT Class 8 Maths Textbook Chapter 9 With Answer Book PDF Free Download
Chapter 9: Algebraic Expressions And Identities
9.1 What are Expressions?
In earlier classes, we have already become familiar with what algebraic expressions (or simply expressions) are. Examples of expressions are:
x + 3, 2y – 5, 3×2, 4xy + 7 etc.
You can form many more expressions. As you know expressions are formed from variables and constants.
The expression 2y – 5 is formed from the variable y and constants 2 and 5. The expression 4xy + 7 is formed from variables x and y and constants 4 and 7.
9.2 Terms, Factors, and Coefficients
Take the expression 4x + 5. This expression is made up of two terms, 4x and 5. Terms are added to form expressions.
Terms themselves can be formed as the product of factors. The term 4x is the product of its factors 4 and x. The term 5 is made up of just one factor, i.e., 5.
The expression 7xy – 5x has two terms 7xy and –5x. The term 7xy is a product of factors 7, x, and y. The numerical factor of a term is called its numerical coefficient or simply coefficient.
The coefficient in the term 7xy is 7 and the coefficient in the term –5x is –5.
9.3 Monomials, Binomials, and Polynomials
The expression that contains only one term is called a monomial. An expression that contains two terms is called a binomial. An expression containing three terms is a trinomial and so on.
In general, an expression containing, one or more terms with a non-zero coefficient (with variables having nonnegative exponents) is called a polynomial. A polynomial may contain any number of terms, one or more than one
| Author | NCERT |
| Language | English |
| No. of Pages | 16 |
| PDF Size | 284 KB |
| Category | Mathematics |
| Source/ Credits | ncert.nic.in |
NCERT Solutions Class 8 Maths Chapter 9 Algebraic Expressions And Identities
Q1. Identify the terms, their coefficients for each of the following expressions. (i) 5xyz2 – 3zy (ii) 1 + x + x2(iii) 4x2y2 – 4x2y2z2 + z2 (iv) 3 – pq + qr – p (v) (x/2) + (y/2) – xy (vi) 0.3a – 0.6ab + 0.5b
Solution :
| Sl. No. | Expression | Term | Coefficient |
| i) | 5xyz2 – 3zy | Term: 5xyz2Term: -3zy | 5 -3 |
| ii) | 1 + x + x2 | Term: 1 Term: x Term: x2 | 1 1 1 |
| iii) | 4x2y2 – 4x2y2z2 + z2 | Term: 4x2y2 Term: -4 x2y2z2 Term : z2 | 4 -4 1 |
| iv) | 3 – pq + qr – p | Term : 3 -pq qr -p | 3 -1 1 -1 |
| v) | (x/2) + (y/2) – xy | Term : x/2 Y/2 -xy | ½ 1/2 -1 |
| vi) | 0.3a – 0.6ab + 0.5b | Term : 0.3a -0.6ab 0.5b | 0.3 -0.6 0.5 |
2. Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories?x + y, 1000, x + x2 + x3 + x4 , 7 + y + 5x, 2y – 3y2 , 2y – 3y2 + 4y3 , 5x – 4y + 3xy, 4z – 15z2 , ab + bc + cd + da, pqr, p2q + pq2 , 2p + 2q
Solution:
Let us first define the classifications of these 3 polynomials:
Monomials Contain only one term.
Binomials, Contain only two terms.
Trinomials, Contain only three terms.
| x + y | two terms | Binomial |
| 1000 | one term | Monomial |
| x + x2 + x3 + x4 | four terms | Polynomial, and it does not fit in listed three categories |
| 2y – 3y2 | two terms | Binomial |
| 2y – 3y2 + 4y3 | three terms | Trinomial |
| 5x – 4y + 3xy | three terms | Trinomial |
| 4z – 15z2 | two terms | Binomial |
| ab + bc + cd + da | four terms | Polynomial, and it does not fit in listed three categories |
| pqr | one term | Monomial |
| p2q + pq2 | two terms | Binomial |
| 2p + 2q | two terms | Binomial |
| 7 + y + 5x | three terms | Trinomial |
NCERT Class 8 Maths Textbook Chapter 9 With Answer Book PDF Free Download