# Class 9 – Algebra

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## Online Tests

Topic Sub Topic Online Practice Test
Algebra
• Review of algebra
• Remainder theorem
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Algebra
• Factor theorem
• Cyclic expressions
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## Study Material

 Algebraic Expression: A combination of literals and numbers connected by one or more of the symbols +, –, ×, and ÷ is called an algebraic expression. The several parts of an algebraic expression separated by + or – sign are called the terms of the expression. Example: , , . Various types of Algebraic Expressions: i) Monomial: An algebraic expression having only one term is called a monomial. Example:,……. are monomials. ii) Binomial: An algebraic expression having two terms is called a binomial. Example: , , ,…..are binomials. iii) Trinomials: An algebraic expression having three terms is called a trinomial. Example: , ,……. are trinomials. iv) Multinomial: An algebraic expression having more than 3 terms is called a multinomial. Example: , , ……. are multinomials. Polynomial: An algebraic expression in which the powers of variables are all whole numbers is called a polynomial. Example: , , ……. are polynomials. But is not a polynomial, as is not a whole number. General Form: The general form of a polynomial in one variable of degree ‘n’ is as follows Where n is a whole number and are real numbers. Degree of a polynomial: The degree of a polynomial in one variable is the highest power of the variable and for a polynomial with multiple variables is the highest sum of all the powers in a single term. Example: i) Degree of ii) Degree of is 4

Operations on polynomials:

The sum of two polynomials is again apolynomial.

Subtraction: To subtract a polynomial from another,change the sign of each term in the expression to be subtracted and then add the two polynomials.

Example: Subtract from

Multiplication: To multiply two or more polynomials multiply the numerical co-efficient and variables separately and write alltogether.

i) Multiply 4ab and -3a2b.

ii) Multiply

Division: If p(x) is a polynomial in x andq(x) is another polynomial in x then the product of these two polynomials is another polynomial say g(x) then we can write

Example:

i) Divide by

ii) Divide by

Identity: An equation that is true for all valuesof the variables is called an Identity.

Example: is true for all values of ‘x’.Here are a few identities listed below.

Important Identities:

i)

ii)

iii)

iv)

v)

vi)

vii)

viii)

ix)

x)

xi)

xii)

xiii)

1. Expand .

Solution:

2. Simplify by using anidentity.

Solution:

We know that

3. If then find .

Solution:

4. Expand

Solution:

We know that

5. If then show that

Solution: (given)

We know that

Hence proved.

We know the identity: …(1)

Consider

From (1) and (2)