Multiplication of algebraic expressions

It tells the introduction and basics of the multiplication of algebraic expressions

3. Continue…
The word algebra comes from the title of the Arabic
book Ilmal-jabrwa’lmukābalaby the Persian mathematician
and astronomer al-Khwarizmi. Algebra is the study of
mathematical symbols and rules for calculating these
symbols. In arithmetic, only numbers and their arithmetical
operations (such as +, −, ×, ÷) occur. In algebra, numbers are
often represented by symbols called variables.

4. ALGEBRAIC EXPRESSIONS
Analgebraicexpressionisacombinationof
constantsandvariablescombinedtogetherwiththehelpof
thefourfundamentalsigns.
Anyrealnumberisaconstant.
1,5,–32,73,2-,8.432,1000000andsoon.
Letters used for representing unknown real numbers
called variables. Variables are x, y, a, b and so on

5. Types of expressions
MONOMIAL
An expression
with one term is
called a
monomial,
Examples
4x, 3�
2
y, − 2�
2
BINOMIAL
An expression
with two term is
called a binomial
Examples
2x + 3, 5�
2
+ 9y,
�
2
�
2
+ 2b .
TRINOMIAL
An expression
with three term
is called a
trinomial
Examples
2�
2
b− 8ab + �
2
,
�
2
− n2 + 3 .

6. Some operations on algebraic expression
ADDITION SUBTRACTION
MULTIPLICATION DIVISION

7. MULTIPLICATION OF ALGEBRIC
EXPRESSIONS
Before doing the product of algebraic expressions, we
should follow the steps given below.
Step 1
•Multiply the signs of the terms.Theproduct of two like signs
are positive and the product of two unlike signs are negative.
step2
•Multiply the corresponding co-efficientsof the terms.
step3
•Multiply the variable factors by using laws of exponents.

8. There are four ways of multiplication on
algebraic expressions.
They are:
Product of a Monomial with a Monomial
Product of a Polynomial with a Monomial
Product of a Binomial with a Binomial
Product of a Polynomial with a Polynomial

9. EXAMPLE: Product of 2�
2
�
2
, 3�
2
z and –�
2
�
3
(2�
2
�
2
)×(3�
2
�)×(−�
2
�
3
)
=(+) ×(+) ×(−)(2 ×3 ×1)(�
2
�
3
)(�
2
�
2
)(z �
2
)
= −6�
5
�
4
�
3
This is how multiply a monomial by a monomial

10. Example :Multiply (3xy + 7) by ( −4y )
(−4y) ×(3xy + 7) =(−4y)×(3xy) +(−4y)×(7)
= (−)×(+)(4 ×3)(x )(y ×y )+ (−4×7)(y)
= −12x�
2
−28y
This is how multiply a polynomial by a monomial

11. Example : Multiply(2x + 5y) and (3x −4y)
(2x + 5y) (3x −4y) = (2x)×(3x −4y) + (5y)×(3x −4y)
= 2×3�×�−2×4�×�+5×3
�×�−(5×4)(�×�)
= 6�
2
−8xy +15xy −20�
2
= 6�
2
+ 7xy −20�
2
(simplify the like terms)
This is how multiply a monomial by a monomial

12. CONCLUTION
We use algebra quite frequently in our
everyday lives, and without even
realizing it We not only use algebra, we
actually need algebra, to solve most of
our problems that involves calculations.