Page 165 - Maths Class 06

Polynomials
An expression containing two or more terms is known as polynomial.

Terms

(a) Like Terms and Unlike Terms
Like terms : The terms having the same literal factors are called NOTE
like terms or similar terms. Such as in the expression
2
2
2
2
2
2
2
4x y - 3yx + 7y x - 8x y, we have 4x y, - 3yx and -8x y as Instead of writing 1 x, write x only.
like or similar terms. The product of x and y can be
written as yx or xy.
Unlike terms : The terms not having same literal factors are called
2
2
3
3
unlike or dissimilar terms. Such as in the expression 5x y - 3x y - 7, we have 5x y and -3x y as unlike
or dissimilar terms.
(b) Powers of Literal
2
In a , a is the base and 2 is the exponent.
EXAMPLE 7. Find out the base and exponent of the following:
(i) b 2 (ii) c 3
2
SOLUTION : (i) In b , b is the base and 2 is the exponent.
3
(ii) In c , c is the base and 3 is the exponent.
Application of Algebraic Expressions in Practical Problems

We come across many practical situations in which algebraic expressions are useful. Some such practical
situations are given below:

Situation Variable Statement using expression

1. Arun has 7 more balls than Nikhil. Let Nikhil has m balls. Arun has (m + 7) balls.

2. Shivam gets 20 marks less than Let Shikha get x marks. Shivam gets (x – 20) marks.
Shikha.

3. Nitin is 4 years older than Akhil. Let Akhil’s age be n years. Nitin’s age is (n + 4) years.

4. Anil is thrice as old as Sudha. Let Sudha’s age be n years. Anil’s age is 3n years.

5. The age of Shilpa’s mother is 3 years Let Neha’s age be n years. The age of Shilpa’s mother is
more than twice of Neha’s age. (2n+ 3) years.

EXAMPLE 8. Write each of the following in the form of algebraic expression:

(a) Five more than thrice of a
(b) Four times a is five less than b.
(c) The product of a and b divided by 9.

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