This document provides an introduction to basic algebra concepts including: - Algebraic expressions which represent operations using numbers, symbols, and variables. - Variables represent unknown quantities in expressions. - Evaluating expressions involves substituting numbers for variables. - Like terms can be added, unlike terms cannot. - Monomials have one term, binomials have two, trinomials have three, and polynomials have more than three. - Identities are equalities that are always true, unlike 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. Likeandunliketerms
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:
Unliketermsare two or more terms that are not like terms,
i.e. they do not have the same variables or powers.
Example: 3abcand 3ghiare unlike terms because they
have different variables

7. Difference between like andunlike 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
Morethan
Increased
Plus
Altogether

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

10. Termsandcoefficients
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