Lesson 3.5 focuses on multiplying polynomials, covering the methods for multiplying monomials with monomials, monomials with polynomials, and binomials with binomials or trinomials. Key concepts include the use of the distributive property and the FOIL method for simplification. The lesson provides examples and exercises for practice in different multiplication methods.

1. LESSON 3.5: MULTIPLYING
POLYNOMIALS

2. LESSON 3.5: MULTIPLYING
POLYNOMIALS
WARM UP ACTIVITY:
I. Simplify
1.
2.
3.
4.
5.

3. LESSON 3.5: MULTIPLYING
POLYNOMIALS
A.
MONOMIAL BY A MONOMIAL
B
MONOMIAL BY A POLYNOMIAL
C BINOMIAL BY A BINOMIAL
D BINOMIAL BY A TRINOMIAL

4.  Monomial – an algebraic expression consisting of one
term but can have multiple variables and a higher degree.
degree
coefficient
variable/s
A. MONOMIAL BY A MONOMIAL
In monomial, the each term consist of only multiplication and exponential operations. There are no
addition, subtraction, or division operations within a single monomial.
LESSON 3.5: MULTIPLYING POLYNOMIA

5.  To multiply two or more monomials, multiply the numerical
coefficients and apply the laws of exponents for product.
Examples:
1.
Solution:
A. MONOMIAL BY A MONOMIAL
 PRODUCT OF POWERS
 POWER OF A POWER
 POWER OF A PRODUCT
LESSON 3.5: MULTIPLYING POLYNOMIA

6. Examples:
2.
Solution:
A. MONOMIAL BY A MONOMIAL
3.
Solution:
)
LESSON 3.5: MULTIPLYING POLYNOMIA

7. Examples:
4. 5.
Solution: Solution:
A. MONOMIAL BY A MONOMIAL
LESSON 3.5: MULTIPLYING POLYNOMIA

8. Examples: Let’s Try:
6. 7.
Solution: 8.
9.
( 10. )
A. MONOMIAL BY A MONOMIAL
LESSON 3.5: MULTIPLYING POLYNOMIA

9.  Polynomial – an algebraic expression of two or more terms
composed of coefficients, variables, exponents, constants, and
operations (except for division by variables/contain variables in the
denominator).
operations
exponent
variables constant
coefficients
B. MONOMIAL BY A
POLYNOMIAL
LESSON 3.5: MULTIPLYING POLYNOMIA

10. To multiply a monomial by a polynomial, use the distributive property of
multiplication over addition observing the law of exponents for product.
Examples:
Solution:
B. MONOMIAL BY A
POLYNOMIAL
LESSON 3.5: MULTIPLYING POLYNOMIA

11. Examples:
2.
Solution:
B. MONOMIAL BY A
POLYNOMIAL
LESSON 3.5: MULTIPLYING POLYNOMIA

12. Examples:
3.
Solution:
]
B. MONOMIAL BY A
POLYNOMIAL
LESSON 3.5: MULTIPLYING POLYNOMIA

13. Examples:
3.
Solution:
B. MONOMIAL BY A
POLYNOMIAL
LESSON 3.5: MULTIPLYING POLYNOMIA

14. Let’s Try
4.
5.
6.
7.
8.
B. MONOMIAL BY A
POLYNOMIAL
LESSON 3.5: MULTIPLYING POLYNOMIA

15. Binomial – a type of polynomial that consists exactly two
terms.
exponent
constant
coefficients
variable
operation (+/-)
C. BINOMIAL BY A BINOMIAL
LESSON 3.5: MULTIPLYING POLYNOMIA

16.  To multiply binomial, simply
distribute the 1st
term of the 1st
binomial to each term of the
other binomial then distribute the
second term to each term of the
other binomial and simplify the
results by combining similar
terms. (FOIL METHOD)
C. BINOMIAL BY A BINOMIAL
20
x 46
_______
120
80
_______
920
Another way is the VERTICAL
METHOD of multiplying. It’s same
as multiplying integers.
LESSON 3.5: MULTIPLYING POLYNOMIA

17. Examples:
1.
FOIL METHOD: F 0 I L
4x + 2
combine similar terms
C. BINOMIAL BY A BINOMIAL
LESSON 3.5: MULTIPLYING POLYNOMIA

18. Examples:
1.
Vertical Method :
__________________
_______________________
C. BINOMIAL BY A BINOMIAL
LESSON 3.5: MULTIPLYING POLYNOMIA

19. Examples:
1.
FOIL METHOD: F 0 I L
)()+ (2)(-1)()+(3)(4)()+(3)(-1)
)]+ [(2)(-1)()]+[(3)(4)()]+[(3)(-1)]
)( + (-2)()+(12)()+(-3)
-3
combine similar terms
C. BINOMIAL BY A BINOMIAL
LESSON 3.5: MULTIPLYING POLYNOMIA

20. Examples:
2.
Vertical Method :
__________________
_______________________
C. BINOMIAL BY A BINOMIAL
LESSON 3.5: MULTIPLYING POLYNOMIA

21. Let’s Try!
1.
2.
C. BINOMIAL BY A BINOMIAL
LESSON 3.5: MULTIPLYING POLYNOMIA

22.  TRINOMIAL - a type of polynomial with exactly three terms.
exponent operations (add & sub)
constant
coefficients
variable(s)
D. BINOMIAL BY A TRINOMIAL
LESSON 3.5: MULTIPLYING POLYNOMIA

23.  To multiply a binomial with more than one
term by a polynomial with three or more
terms, simply distribute the first term of the
first polynomial to each term of the other
polynomial. Repeat the procedure up to the
last term and simplify the results by
combining similar terms.
D. BINOMIAL BY A TRINOMIAL
LESSON 3.5: MULTIPLYING POLYNOMIA

24. Examples: Find the product
Using Distributive Property:
D. BINOMIAL BY A TRINOMIAL
combine similar terms
=6x2 +8xy +5
+20y
+2x +15x
=6x2 +8xy +5
+20y
+17x
LESSON 3.5: MULTIPLYING POLYNOMIA

25. Examples: Find the product
Using Vertical Method:
_____________________
D. BINOMIAL BY A TRINOMIAL
combine similar terms
15x +20y +5
6x2
+8xy +2x
6x2
+8xy +17x +5
+20y
15x
+2x
LESSON 3.5: MULTIPLYING POLYNOMIA

26. Examples: Find the product
2.
Using Distributive Property:
D. BINOMIAL BY A TRINOMIAL
= 9x2
-12xy +15xz -8y
+6x +10z
LESSON 3.5: MULTIPLYING POLYNOMIA

27. Examples: Find the product
Using Vertical Method:
_____________________
D. BINOMIAL BY A TRINOMIAL
6x +8y +10z
9x2
-12xy +15xz
9x2
+15xz+6x +10z
+8y
Although, and are aligned and are
also aligned, we cannot combine
them because they are not similar.
-12xy
LESSON 3.5: MULTIPLYING POLYNOMIA

28. Examples: Find the product
3.
Using Distributive Property:
combine similar terms
D. BINOMIAL BY A TRINOMIAL
= 6x2
+ xy -4xz -35 -10yz
LESSON 3.5: MULTIPLYING POLYNOMIA

29. Examples: Find the product
3.
Using Vertical Method:
___________________
--------
----------------
____________________________
D. BINOMIAL BY A TRINOMIAL
Although, and are aligned, we
cannot combine them because they
are not similar.
6x2
+xy-4xz -10yz
+35
LESSON 3.5: MULTIPLYING POLYNOMIA

30. LET’S TRY THIS OUT!
)
D. BINOMIAL BY A TRINOMIAL
LESSON 3.5: MULTIPLYING POLYNOMIA

31. A. Instruction: Find the product of the following expressions using
Distributive Method
1. 3m2
n3
(4mn4
) 2. 5xy3. 7k (3k3
- 2k2
+7)
B. Instruction: Find the product of the following expressions using
FOIL Method
4. (2x+3)(3x+1) 5. (2x2
– 3y4
)(3x3
+y2
)
C. Instruction: Find the product of the following expressions using
Vertical Method
6. (3x+9y)(2x+5y – 4z)
7. (3x+9y)(2x2
-5y2
– 4z2
)
Assignment 3.6
LESSON 3.5: MULTIPLYING POLYNOMIA

32. THANK YOU!