Algebra introduces algebraic expressions and their components. An algebraic expression contains variables, numbers, and operations. A variable represents an unknown quantity. Terms are the parts of an expression separated by plus and minus signs, and coefficients are numbers that multiply variables. Expressions can be simplified by combining like terms that have the same variables and powers. Polynomials contain more than three terms, while monomials, binomials, and trinomials have one, two, or three terms respectively. Identities are equations that are always true, unlike standard equations.

1. ALGEBRA

2. INTRODUCTION
Algebraic expression – a group of
numbers, symbols, and variables that express an
operation or a series of operations.
EXAMPLES: a-8
b-2
z+12 etc……

3. DEFINITIONS
Variable – A variable is a letter or symbol
that represents a number. It is an unknown
quantity
EXAMPLES: 5+z=13
4-y=1 etc……

4. Evaluating an algebraic
expression –
To find the value of an algebraic expression we can
substitute numbers for variables.
Examples: m+7,m-3 etc…
(‘m’ variable can be any number)
m + 8 if m = 2 then 2 + 8 = 10
z – 6 if z = 10 then 10 - 6 = 4

5. Like and unlike terms
Like terms:
like terms are terms that have the
same variables and powers
Example: 8xyz2 and 5xyz2 are like terms
because they have the same variables
and power

6. unlike terms:
Unlike terms are two or more terms that are not like terms,
i.e. they do not have the same variables or powers.
Example: 3abc and 3ghi are unlike terms because they
have different variables

7. Difference between like and unlike terms
1.Like terms can be added together to simplify an expression.
2.When adding like terms, add the numerical coefficients and
retain the variable.
3.Unlike terms cannot be added together since the variables
represent different items.

8. Words That Lead to
Addition
Sum
More than
Increased
Plus
Altogether

9. Words That Lead to
Subtraction
Decreased
Less
Difference
Minus
How many more

10. Terms and coefficients
Terms:
Terms are the elements separated by the plus or minus
signs.
Example: 3x2+2y+7xy+5
This example has four terms, 3x2, 2y, 7xy, and 5.

11. Coefficients:
A number used to multiply a variable.
Example: 6z means 6 times z, and "z" is a variable, so
6 is a coefficient.

12. Monomials,binomials,trinomials
and
polynomials
Monomial:
An expression with one term is called a monomial
Binomial:
An expression with two terms is called a binomial

13. Trinomial:
An expression with three terms is called a
trinomial
Polynomial:
A polynomial is an expression consisting of
variables and coefficients more than three
terms.

14. Examples:
,

15. Identity
1. An identity is an equality, which is true for all
values of the variables in the equality
2. An equation is not an identity.

16. Standard identities
1) (a+b)2 = a2 + 2ab + b2
2) (a-b)2 = a2-2ab + b2
3) (a+b) (a-b) = a2-b2
4) (x+a)(x+b)=x2 +(a+b)x+ab

17. Ten more than a number n+10
A number decrease by 5 w-5
6 less than a number z-6
A number increased by 8 n+8
The sum of a number & 9 n+9
4 more than a number y+4

18. A number s plus 2 s+2
A number decrease by 1 k-1
31 less than a number x-31
A number b increased by 7 b=7
The sum of a number & 6 n=6
9 more than a number z=9

19. Prepared by
G.SRI HARSHA
VIII D