The document defines and provides examples of algebraic expressions, variables, terms, coefficients, and different types of algebraic expressions such as monomials, binomials, trinomials, and polynomials. It also discusses the differences between like and unlike terms and provides examples of how like terms can be combined through addition while unlike terms cannot. Standard algebraic identities are presented as well.

1. Algebraic Expressions.
Name: A.Yodha
Gopaal.

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. 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

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

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.

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,

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,trinomial
s 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 +
b 2
2) (a-b) 2 = a2-2ab + b2
3) (a+b) (a-b) = a2- b 2
4) (x+a)(x+b)=x 2
+(a+b)x+ab

17. We can also write Algebraic
Expressions for These Word
Phrases
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 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