This document discusses algebraic expressions and identities. It defines expressions as combinations of numbers and variables connected by operation signs. Expressions can be monomials containing one term, binomials containing two terms, or trinomials containing three terms. Terms are separated parts of expressions and factors are the numbers within terms. Coefficients are factors without signs. The document also covers adding, subtracting and multiplying expressions, as well as defining identities as equalities that are true for all variable values. It provides examples of standard identities for the sum and difference of squares and multiplying the sum and difference of two terms.

1. AlgebrAic
expressions
And
identities
done by
ANKIT SAHOO
And
Lalatendu l. soren
Class
Viii-d

2. What are
expressions?
A combination of numbers and
variables
Connected by the signs of
operations
(addition,subtraction,multiplicatio
n,division) is called an algebraic
expressions.
3 4

3. Terms,factors and coefficients
Various parts of algebraic expressions which
are separated by signs + or – are called the
terms of the expressions.
Each term of an algebraic expression is a
product of one or more numbers know as the
factor of that term.
 IN A TERM OF AN ALGEBRAIC
EXPRESSION ANY OF THE FACTOR WITHOUT
SIGN OF THE TERM IS CALLED COEFFICIENT
OF THE PRODUCT OF THE OTHER FACTOR

4. exAmples
EXAMPLE
2X-4XY
TERMS=2X,-4XY
FACTORS OF 2X=2 and X
FACTORS OF -4XY=-4,X and Y
In 2x ,Coefficient of x is 2 and that of 2 is x.

5. Types of expressions
MONOMIALS
THE EXPRESSION WHICHCONTAINS ONLY ONE TERMIS
CALLEDMONOMIAL.
EXAMPLE 6XY2
BINOMIALS
THE EXPRESSIONS THAT CONTAINS TWO UNLIKE TERMS
IS CALLEDBINOMIAL.
EXAMPLE 4XY+ 5XY
TRINOMIALS
THE EXPRESSION CONTAINING
THREE UNLIKE TERMS IS CALLED TRINOMIAL.
EXAMPLE 4XY + 9XY – 8XY2

6. TERMS AND
UNLIKE
TERMS
EXAMPLES
3X2
AND 7X2
LIKE
TERM
 6W AND 6Y UNLIKE
TERMS
 5,85 AND 100 LIKE
TERMS
 4X AND 4XY UNLIKE
TERMS
THE TERMS
HAVING THE
SAME LITERAL
FACTORS ARE
CALLEDLIKE
TERMOTHER
WISE THEY ARE
CALLED
UNLIKE TERMS

7. ADDITION OF
ALGEBRAIC
EXPRESSIONS
 In adding algebraic expressions , we collect
different groups of like terms and find the sum
of like terms in each group.
Example(7x-4x+5)+(5x-x+9)
=7x+5x-4x-x+5+9
=12x-5x+14
=7x+14.

8. Subtraction of
algebraic expressions
In orderto subtract an algebraic expression from
another,we change the signs(from+ to – orfrom–
to +) of all the terms of the expressions which is to
subtracted and then the two expressions are added.
Example(7x-4x+5)-(5x-x+9)
=7x-4x+5-5x+x-9
=3x-5x+5-9
=-2x-4

9. MULTIPLICATION OF
ALGEBRAIC
EXPRESSIONS.
MULTIPLICATION OF A MONOMIAL BY A TRINOMIAL
EX. MULTIPLY : 3p x (4p2
+ 5p + 7)
=(3p x 3p2
) + (3p x 5p) + (3p x 7)
= 9p3
+ 15p2
+ 21p
……………….THIS IS HOW WE MULTIPLY A MONOMIAL BY A TRINOMIAL.
MULTIPLICATION OF TWO BINOMIALS
EX: MULTIPLY – (3x + 2y) and (5x + 3y)
= (3x + 2y) x (5x + 3y)
= 3x x (5x + 3y) + 2y x (5x + 3y)
= (3x x 5x + 3x x 3y) + (2y x 5x + 2y x 3y)
= 15x2 + 9xy + 10xy + 6y2
= 15x2 + 19xy + 6y2
……………….THIS IS HOW WE MULTIPLY A MONOMIAL BY A TRINOMIAL.

10. MULTIPLICATION OF A BINOMIAL BY
A TRINOMIAL
EX: MULTIPLY– (a + b) (2a – 3b + c)
(2a - 3b + c)
= a (2a – 3b + c) + b (2a – 3b + c)
= 2a2
– 3ab + ac + 2ab – 3b2
+ bc
= 2a2
– ab + ac – 3b2
+ bc
……………….THIS IS HOW WE MULTIPLY A
MONOMIAL BY A TRINOMIAL.

11. WHAT IS AN
IDENTITY?
AN IDENTITY IS AN
EQUALITY WHICH IS TRUE
FOR ALL VALUES OF THE
VARIABLE(s).

12. STANDARD
IDENTITIES
IDENTITIY 1IDENTITIY 1
((a + b)a + b)22
= a= a22
+ 2ab + b+ 2ab + b22
i.e., Square of the sum of two terms =i.e., Square of the sum of two terms =
(Square of the first term) + (Square of(Square of the first term) + (Square of
the second term) + 2 x (First term) xthe second term) + 2 x (First term) x
(Second term)(Second term)
Proof:Proof: (a + b)(a + b)22
= (a + b)(a + b)= (a + b)(a + b)
=a(a+b)+b(a+b)=a(a+b)+b(a+b)
=a=a22
+ab+ba+b+ab+ba+b22
=a=a22
+2ab+b+2ab+b22

13. IDENTITIY 2
(a - b)2
= a2
- 2ab + b2
i.e., Square of the difference of two
terms = (Square of the first term) +
(Square of the second term) + 2 x (First
term) x (Second term)
Proof: (a - b)2
= (a - b)(a - b)
=a(a-b)-b(a+b)
=a2
-ab-ba+b2
=a2
-2ab+b2

14. IDENTITIY 3
(a + b)(a - c) = a2
– b2
i.e., (First term + Second term) (First term -
Second term) = (First term)2 – (Second term)2
Proof: (a + b)(a - b) = a (a - b) + b (a - b)
= a2
- ab + ba – b2
= a2
– ab + ab – b2
= a2
– b2