1. An algebraic expression is a combination of numbers, variables, and operation symbols. It can be classified as a monomial, binomial, or trinomial based on the number of terms. 2. Like terms contain the same variables raised to the same powers, while unlike terms do not. Multiplication of algebraic expressions follows rules such as the product of like signs being positive and unlike signs being negative. 3. There are special product identities for multiplying binomials and factoring algebraic expressions through grouping and finding greatest common factors. Division of algebraic expressions also follows rules regarding the signs of the quotient.

1. ALGEBRAIC
EXPRESSIONS

2. WHAT IS ALGEBRAIC EXPRESSION?
 A number or a combination of numbers
connected by the symbols of operation
+,-,*,/ is called an algebraic
expression.
E.g.- 3x, 2x, -3/5x . The no’s 3, 2, -
3, -3/5 used above are constants and
the literal no’s x, y, z are variables.
The several parts are called terms.
The signs + and – connect the
different terms.
2x and -3y are terms of the

3. WHAT ARE MONOMIAL, BINOMIAL
AND TRINOMIAL?
An expression having only one term is
called monomial.
E.g.- 3x, -4y, 2/3yz are monomials.
An expression having two terns is called
binomial.
E.g.- 2x -3y, 4x + 5xz are
binomials.
An expression having three terms is
called trinomial.
E.g.- -3p + 5q -2/5pq, 7a - 2abc –

4. WHAT ARE LIKE AND UNLIKE TERMS?
 Terms having same combinations of
literal numbers are called like terms.
 Terms do not having same combinations
of literal numbers are called unlike
terms.
For e.g.-
1. 4ab, -3ba = Like terms
2. 3xy, -5ya = Unlike terms
3. 6 abc, -5acd = Unlike terms
4. 8pq, -3qp = Like terms

5. WHAT IS MULTIPLICATION OF
ALGEBRAIC EXPRESSIONS?
 The product of two numbers of like signs is
positive and the product of two numbers of
unlike signs is negative.
For E.g., -
3 x 5 = 15; -4/5 x -5/3
= 4/3
-4 x 2 = -8; 3 x (-4/3) =
-4
We also know the following laws of
exponents
 a x a = a
 (a ) = a

6. WHAT IS MULTIPLICATION OF A
MONOMIAL BY A MONOMIAL?
 The product of two monomials is
obtained by the application of the
laws of exponents and the rules of
signs, e.g.,
 2x y³ X 3x² y³ = (2x3) x X y
= 6x y
 Thus we have the following rules-
1. The numerical coefficient of the
product of two or more monomials is
equal to the product of their
numerical coefficients.
2. The variable part of the product

7. WHAT IS MULTIPLICATION OF A
BINOMIAL BY A MONOMIAL?
 To multiply a binomial by a monomial, we
use the following rule-
a x (b + c) = a x b + a x c
For E.g.-
Multiply: 4b + 6 by 3a
Product = 3a(4b + 6)
= 3a x 4b + 3a x 6
= 12ab + 18a

8. WHAT IS MULTIPLICATION OF A
TRINOMIAL BY A MONOMIAL?
To multiply a trinomial by a monomial,
we use the following rule:
a x (b + c + d) = a x b + a x c + a x d
For e.g. –
Multiply: 3x – 2x + 2 by 3x
Product = 3x(3x – 2x + 2)
= 3x x 3x – 3x x 2x
+ 3x x 2
= 9x² - 6x² + 6x

9. WHAT IS MULTIPLICATION OF A
POLYNOMIAL BY A POLYNOMIAL?
 Let us multiply two binomials (4x – y) and
(3x – 2y). Here we will use the law of
multiplication of a binomial by a monomial
twice. Consider (4x – y) as one number.
Then (4x – y) (3x –
2y) = (4x –y) x 3 + (4x –y) x (-2y)
= 4x x 3x – y x 3x -4x x 2y
+ y x 2y
=12x² - 3xy – 8xy + 2y²
= 12x² - 11xy + 2y² .

10. WHICH ARE SPECIAL PRODUCTS
(IDENTITIES)?
The four special identities are:
1. (x + a) (x + b) = x + (a + b)x + ab
For e.g. –
(x + 3) (x + 2)
= x + (3 + 2)x + 3 x
2
= x + 5x + 6
2. (a + b) = a + b + 2ab
For e.g. –
(3p + 4q) (3p + 4q)
= (3p)² + (4q)² + 2
x 3p x 4q
= 9p² + (16q)² +

11. 3. (a – b) = a + b - 2ab
For e.g.-
(3p – 4q) (3p – 4q)
= (3p)² + (4q)² -2 x
3p x 4q
= (9p)² + (16q)² -
24pq.
4. (a - b ) = (a + b) (a – b)
For e.g.-
(a – b) - (a + b)
= (a – b + a + b) (a –
b – a – b)
=2a x (-2b)
=-4ab.

12. WHAT ARE RULES OF SIGNS IN
DIVISION?
1. When the dividend and the divisor have
the same signs, the quotient has the plus
sign.
2. When the dividend and the divisor have
opposite signs, the quotient has the
negative sign.
3. The process of division may be divided in
three cases:
 Division of a monomial by another
monomial.
 Division of a polynomial by monomial.

13. WHAT IS FACTORIZATION OF
ALGEBRAIC EXPRESSIONS?
The factors of-
 a+ 2ab + b are (a+b) (a+b)
 A – 2ab + b are (a-b) (a-b)
 A -b are (a-b) (a +b)
 4x are-
1. 4 X x²
2. 2 X 2 X x²
3. 2 X 2 X x X x
4. 4 X x X x
 1 is a factor of every algebraic term, so 1 is
called a trivial factor.

14. HOW DO WE DO FACTORIZATION BY
REGROUPING TERMS?
 Sometimes it is not possible to find the
greatest common factor of the given set of
monomials. But by regrouping the given terms,
we can find the factors of the given
expression.
For e.g.,-
3xy + 2 + 6y + x = 3xy + 6y + x + 2
= 3y(x + 2)
+ 1(x + 2)
=(x + 2)
(3y + 1)