Class 9 – Algebra
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Algebra 

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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:
Addition: To add two or more polynomials, group the like terms and add their constant coefficients.
The sum of two polynomials is again apolynomial.
Example: Add
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 coefficient 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)