This document provides an overview of algebraic expressions and identities. It defines terms, factors, coefficients, monomials, binomials, polynomials, like and unlike terms. It explains how to perform addition, subtraction, multiplication, and division of algebraic expressions. It also defines what an identity is and how to apply identities.

1. MATHS
PROJECT
Made by :- shubham
Class:- viii-c

2. ALGEBRAIC EXPRESSION
AND
IDENTITIES

3. INDEX
• Expression
• Term, factors and coefficient
• Monomial, binomials and polynomials
• Like and unlike terms
• Addition and subtraction in algebra
• Multiplication in algebra
• What is an identity?
• Applying identities

4. Expression
• Numbers, symbols and operators (such as + and ×)
grouped together that show the value of
something.
Example: 2×3 is an expression

5. Terms, factors and coefficient
Terms :- In Algebra a term is either a single number or
variable, or numbers and variables multiplied
together.
Terms are separated by + or − signs

6. Factors :-Factors are numbers you can multiply together
to get another number:
Example: 2 and 3 are factors of 6, because 2 × 3 = 6. A
number can have MANY factors!
Example: What are the factors of 12?
3 and 4 are factors of 12, because 3 × 4 = 12.
Also 2 × 6 = 12 so 2 and 6 are also factors of 12.
And 1 × 12 = 12 so 1 and 12 are factors of 12 as well.
In Algebra, factors are what you can multiply together to
get an expression.
(x+3) and (x+1) are factors of x2 + 4x + 3:

7. • Coefficient :-A number used to multiply a variable.
Example: 6z means 6 times z, and "z" is a variable,
so 6 is a coefficient.
Sometimes a letter stands in for the number.
Example: In ax2 + bx + c, "x" is a variable, and
"a" and "b" are coefficients.

8. Monomial, binomial and polynomial
• Monomial :- A polynomial with just one term.
Example: 3x2

9. Binomial :- A polynomial with two terms.
Example: 3x2 + 2
Polynomial :-An expression that can have
constants, variables and exponents, that
can be combined using addition,
subtraction, multiplication and division,
but:
• no division by a variable.
• a variable's exponents can only be
0,1,2,3,... etc.
• it can't have an infinite number of terms.

10. Like and unlike terms
• Like terms:- "Like terms" are terms whose variables (and
their exponents such as the 2 in x2) are the same.In
other words, terms that are "like" each other.
• Note: the coefficients (the numbers you multiply by,
such as "5" in 5x) can be different.
Example:
7x + x -2x
Are all like terms because the variables are all x
Example:
(1/3)xy2-2xy2+6xy2
Are all like terms because the variables are all xy2

11. • Unlike terms :-if they are not like terms, they are
called "Unlike Terms":

12. Combining like terms
• You can add like terms together to make one term:
Example: 7x + x
They are both like terms, so you can just add them:
7x + x = 8x
• By the way ... why don't we write "1x" ?
It is just easier to write x. Imagine you were adding eggs:
• 7 eggs plus 1 egg is 8 eggs could be written 7 eggs + egg = 8 eggs
Example: 3x2 - 7 + 4x3 - x2 + 2
Some of the terms are like terms.
Combine like terms:
(3x2 - x2) + (4x3) + (2 - 7)
Then add like terms:
2x2 + 4x3 - 5

13. Addition and subtraction in algebra
• Addition of algebraic expressions :-
while adding algebraic expression we collect the
like terms and add them. The sum of several like
terms is the like terms whose coefficient is the sum
of the coefficient of these like terms.
example :-add: 6a+8b-5c and 2b+c-4a.
Answer:- collecting like terms
6a-4a+8b+2b-5c+c
:-> 2a+10b-4c

14. • Subtraction of algebraic expressions :-
steps for subtraction of algebraic expressions:-
i. arrange the terms of the given expression in the
same order.
ii. Write the given expressions in such a way that the
like terms occur one below the other, keeping the
subtracted in the second row.
iii. Change the sign of each term in the lower row
from+ to – and – to +
iv. With new signs of the terms of lower row, add
column wise

15. • Example :- subtract 4a+5b-3c from 6a- 3b+c
answer :-we have
6a-3b+c
+4a+5b-3c
- - +
2a-8b+4c

16. Multiplication and division in algebra
• Before taking up the product of algebraic
expressions. Let us look at 2 important rules
i. The product of 2 factors with the same signs is
positive and factors with different signs is
negative.
ii. If x is a variable and m and n are positive integers,
then (xᴹ × xᴺ)=x(ᴹ+ᴺ)

17. Multiplication of two monomials
• Rule :- product of 2 monomials
(product of their numerical coefficient)×(product
of their variable parts)
example :- find the product of
(6xy)×(-3xᶾyᶾ)
Answer:- (6×-3) × (xy × xᶾyᶾ)
= -18x⁴y⁴

18. Multiplication of a polynomial by a monomial
• Rule :-multiply each term of the polynomial by the
monomial, using the distributive law
a×(b+c)=a ×b+a ×c
Multiplication of two binomials