It is useful for grad 8

1. Presented by Sundera Kumar
K
Multiplicati
on of
Algebraic
Expressions

2. 2
Learning Objectives
Key Goals for This Chapter
Algebraic Expressions
Understand the different types of
algebraic expressions such as
monomials, binomials, and
polynomials, recognizing their
structure and components.
Multiplication Techniques
Learn how to multiply
monomials, binomials, and
polynomials effectively, applying
the right methods for various
algebraic expressions.
Distributive Property
Apply the distributive property
in multiplication to simplify and
solve algebraic expressions,
enhancing problem-solving skills
in mathematics.

3. Understandin
g Algebraic
Expressions
An algebraic expression is a combination of variables, numbers, and operations. Common
types include monomials (one term), binomials (two terms), and polynomials (multiple
terms) used in calculations.

4. Understandin
g Sign Rules
in
Multiplication
In multiplication, the signs of numbers
determine the result: Positive × Positive =
Positive; Positive × Negative = Negative;
Negative × Negative = Positive. Remembering
these rules is essential for solving problems!

5. Multiplication
of monomials
• We have the 'x' sign for multiplication. It need not be
written between the product of a numeral and a
literal number.(a x y = ay)
• To multiply monomials, multiply the coefficients
and add the exponents of like bases. For example,
(3x^2 times 2x^3 = 6x^{2+3} = 6x^5), showcasing
the process clearly.

6. Rules to be followed to multiply
monomials
i) Numerical coefficient in the product =
product of numerical coefficients in the
monomials
ii) Literal coefficient in the product =
product of literal coefficients in the
monomials
These rules may be extended for the
product of three or more monomials.
Example: 6ab * 4b = (6 * 4)(abb) = 24a * b

7. Multiplying a Monomial by a
Binomial
We know the distributive property a(b+c)=ab+ac or (b+c)a=ba+ca.
This property gives us the method of multiplication of a monomial and a binomial. In order to
multiply a binomial by a monomial, we must multiply each term of the binomial by the
monomial.
This can be done in two ways:
i) Horizontal method example Answer: (6x^{2}+8xy) The problem demonstrates the distributive
property of multiplication over addition. The expression (2x(3x+4y)) is expanded by multiplying
(2x) by each term inside the parentheses separately: Multiply (2x) by (3x) to get (6x^{2}).
Multiply (2x) by (4y) to get (8xy).
Add the results together to get the final expression (6x^{2}+8xy).
ii) Column method example Answer: (6x^{2}+8xy) The problem demonstrates how to multiply
the algebraic expression (3x+4y) by (2x) using the column method. Multiply (4y) by (2x) to get
(8xy). Multiply (3x) by (2x) to get (6x^{2}).
Combine the results to get the final expression (6x^{2}+8xy).

8. Horizontal
Method of
Multiplication
The horizontal method simplifies
multiplication by aligning expressions side-by-
side. This technique enhances understanding,
allowing students to see each step clearly as
they derive the answer visually.

9. Using the
Column
Method
The Column Method simplifies polynomial
multiplication by aligning numbers vertically.
Each term is multiplied step-by-step, ensuring
clarity and organization, making it easier for
students to follow the process visually.

10. Multiplying a
Monomial and
Polynomial

11. Multiplying
Two
Binomials:
Distributive
Method
To multiply two binomials, use the FOIL
method: First, Outer, Inner, and Last. This
systematic approach helps ensure all terms are
multiplied correctly for accurate results.

12. Multiplying
Monomials
Example
Let's explore the multiplication of monomials
with the example 4x × 3x². The product is
found by multiplying the coefficients and
adding the exponents, resulting in 12x³.

13. Multiplying a
Monomial
and
Polynomial
To multiply the monomial 3a with the
polynomial (2a² + 4a + 1), distribute 3a to each
term, producing 6a³ + 12a² + 3a as the result.

14. Multiplying
Monomial by
Binomial
To find the product of 2x(3x + 5), use the distributive
property. Multiply 2x with each term in the binomial
for the final expression 6x² + 10x.

15. Multiplying Binomials
To multiply the binomials:
(x + 3)(x + 4)=x^2+4x+3x+12
= x^2+7x+12

17. What is 3x × 4x?
12x^2
7x^2
10x^2
15x^2

18. What is 5x × 2x?
10x²
7x²
12x
8x²

19. What is 3x × 10?
12x
30x-1
30x
7x^2

20. What is x^3 × 4x?
4x^4
12x^2
12x
7x

21. What is the product of (x+1) and 3x?
6x^2
5x
3x^2+3x
8x^2

22. What is the product of (x+2) and (x-1)?
x^2-x+2
x^2+x-1
x^2-x+2
x^2+x-2

23. What is the product of (x-1) and (x+1)?
x^2-1
x^2+1
x+1
x-1

24. What is the product of (2x-2) and 3x?
6x^2+1
6x^2-6x
6x
6x^2-2

25. What is the product of 2 and 3x+1?
6x^2-1
5x+1
6x+2
8x^2

26. What is the product of -11y^2 and (3y+7)?
-33y^3+11y^2
-33y^3-77y^2
-33y^3+77y^2
33y^3-77y^2

27. Summary of
Key Concepts
In this chapter, we explored key multiplication
rules and the importance of the distributive
property. Continued practice will enhance your
understanding and mastery of algebraic
expressions.