this a complete information on algebraic expressions and identites for class 8

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