4.5 Combining polynomials using multiplication

Page 1 / 2

This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. Operations with algebraic expressions and numerical evaluations are introduced in this chapter. Coefficients are described rather than merely defined. Special binomial products have both literal and symbolic explanations and since they occur so frequently in mathematics, we have been careful to help the student remember them. In each example problem, the student is "talked" through the symbolic form.Objectives of this module: be able to multiply a polynomial by a monomial, be able to simplify +(a + b) and -(a - b), be able to multiply a polynomial by a polynomial.

Overview

Multiplying a Polynomial by a Monomial
Simplifying $+ (a + b)$ and $- (a + b)$
Multiplying a Polynomial by a Polynomial

Multiplying a polynomial by a monomial

Multiplying a polynomial by a monomial is a direct application of the distributive property.

Distributive property

The distributive property suggests the following rule.

Multiplying a polynomial by a monomial

To multiply a polynomial by a monomial, multiply every term of the polynomial by the monomial and then add the resulting products together.

Sample set a

Got questions? Get instant answers now!

$10 a b^{2} c (125 a^{2}) = 1250 a^{3} b^{2} c$

Got questions? Get instant answers now!

Practice set a

Determine the following products.

$3 (x + 8)$

$3 x + 24$

Got questions? Get instant answers now!

$(2 + a) 4$

$4 a + 8$

Got questions? Get instant answers now!

$(a^{2} - 2 b + 6) 2 a$

$2 a^{3} - 4 a b + 12 a$

Got questions? Get instant answers now!

$8 a^{2} b^{3} (2 a + 7 b + 3)$

$16 a^{3} b^{3} + 56 a^{2} b^{4} + 24 a^{2} b^{3}$

Got questions? Get instant answers now!

$4 x (2 x^{5} + 6 x^{4} - 8 x^{3} - x^{2} + 9 x - 11)$

$8 x^{6} + 24 x^{5} - 32 x^{4} - 4 x^{3} + 36 x^{2} - 44 x$

Got questions? Get instant answers now!

$(3 a^{2} b) (2 a b^{2} + 4 b^{3})$

$6 a^{3} b^{3} + 12 a^{2} b^{4}$

Got questions? Get instant answers now!

$5 m n (m^{2} n^{2} + m + n^{0}), n \neq 0$

$5 m^{3} n^{3} + 5 m^{2} n + 5 m n$

Got questions? Get instant answers now!

$6.03 (2.11 a^{3} + 8.00 a^{2} b)$

$12.7233 a^{3} + 48.24 a^{2} b$

Got questions? Get instant answers now!

Simplifying $+ (a + b)$ And $- (a + b)$

$+ (a + b)$ And $- (a + b)$

Oftentimes, we will encounter multiplications of the form

+ 1 (a + b)

- 1 (a + b)

These terms will actually appear as

+ (a + b)

and

- (a + b)

Using the distributive property, we can remove the parentheses.

The parentheses have been removed and the sign of each term has remained the same.

The parentheses have been removed and the sign of each term has been changed to its opposite.

To remove a set of parentheses preceded by a " $+$ " sign, simply remove the parentheses and leave the sign of each term the same.
To remove a set of parentheses preceded by a “ $-$ ” sign, remove the parentheses and change the sign of each term to its opposite sign.

Sample set b

Simplify the expressions.

$(6 x - 1)$ .

This set of parentheses is preceded by a “ $+$ ’’ sign (implied). We simply drop the parentheses.

$(6 x - 1) = 6 x - 1$

Got questions? Get instant answers now!

$(14 a^{2} b^{3} - 6 a^{3} b^{2} + a b^{4}) = 14 a^{2} b^{3} - 6 a^{3} b^{2} + a b^{4}$

Got questions? Get instant answers now!

$- (21 a^{2} + 7 a - 18)$ .

This set of parentheses is preceded by a “ $-$ ” sign. We can drop the parentheses as long as we change the sign of every term inside the parentheses to its opposite sign.

$- (21 a^{2} + 7 a - 18) = - 21 a^{2} - 7 a + 18$

Got questions? Get instant answers now!

$- (7 y^{3} - 2 y^{2} + 9 y + 1) = - 7 y^{3} + 2 y^{2} - 9 y - 1$

Got questions? Get instant answers now!

Practice set b

Simplify by removing the parentheses.

$(2 a + 3 b)$

$2 a + 3 b$

Got questions? Get instant answers now!

$(a^{2} - 6 a + 10)$

$a^{2} - 6 a + 10$

Got questions? Get instant answers now!

$- (x + 2 y)$

$- x - 2 y$

Got questions? Get instant answers now!

$- (5 m - 2 n)$

$- 5 m + 2 n$

Got questions? Get instant answers now!

$- (- 3 s^{2} - 7 s + 9)$

$3 s^{2} + 7 s - 9$

Got questions? Get instant answers now!

Multiplying a polynomial by a polynomial

Since we can consider an expression enclosed within parentheses as a single quantity, we have, by the distributive property,

For convenience we will use the commutative property of addition to write this expression so that the first two terms contain $a$ and the second two contain $b$ .

Questions & Answers

Discuss the differences between taste and flavor, including how other sensory inputs contribute to our perception of flavor.

John Reply

taste refers to your understanding of the flavor . while flavor one The other hand is refers to sort of just a blend things.

Faith

While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma

Kamara

which drugs can we use for ulcers

Ummi Reply

omeprazole

Kamara

what

Renee

what is this

Renee

is a drug

Kamara

of anti-ulcer

Kamara

Omeprazole Cimetidine / Tagament For the complicated once ulcer - kit

Patrick

what is the function of lymphatic system

Nency Reply

Not really sure

Eli

to drain extracellular fluid all over the body.

asegid

The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include: 1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of

asegid

to transport fluids fats proteins and lymphocytes to the blood stream as lymph

Adama

what is anatomy

Oyindarmola Reply

Anatomy is the identification and description of the structures of living things

Kamara

what's the difference between anatomy and physiology

Oyerinde Reply

Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.

AI-Robot

what is enzymes all about?

Mohammed Reply

Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems

Kamara

yes

Prince

how does the stomach protect itself from the damaging effects of HCl

Wulku Reply

little girl okay how does the stomach protect itself from the damaging effect of HCL

Wulku

it is because of the enzyme that the stomach produce that help the stomach from the damaging effect of HCL

Kamara

function of digestive system

Ali Reply

function of digestive

Ali

the diagram of the lungs

Adaeze Reply

what is the normal body temperature

Diya Reply

37 degrees selcius

Xolo

37°c

Stephanie

please why 37 degree selcius normal temperature

Mark

36.5

Simon

37°c

Iyogho

the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature

Stephanie

37A c

Wulku

what is anaemia

Diya Reply

anaemia is the decrease in RBC count hemoglobin count and PVC count

Eniola

what is the pH of the vagina

Diya Reply

how does Lysin attack pathogens

Diya

acid

Mary

I information on anatomy position and digestive system and there enzyme

Elisha Reply

anatomy of the female external genitalia

Muhammad Reply

Organ Systems Of The Human Body (Continued) Organ Systems Of The Human Body (Continued)

Theophilus Reply

what's lochia albra

Kizito

Got questions? Join the online conversation and get instant answers!

Jobilize.com Reply

<< Chapter < Page Page > Chapter >>

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

100% Free Mobile Applications
Receive real-time job alerts and never miss the right job again

Source: OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3

Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask

	2 Multiplying a polynomial by a monomial By OpenStax Read Online Course
	Basic Of Computer Exam By Naveen Tomar Start Quiz
	Business Law Ethics By Kevin Moquin Start Quiz
	Thermal-Fluid Systems MCQ By Steve Gibbs Start Quiz
	14 Biology 14 DNA Structure and Function MCQ By OpenStax Start Quiz
	Anthropology Life Cycle By Richley Crapo Start Assignment
©flickr: Bertram	Chemistry Ch 1 2 Test 1 By Madison Christian Start Quiz
	Microeconomics Practice MCQ By Frank Levy Start Test
	2 AP Key Terms 02 Chemical Level of Organization By OpenStax Start Key Terms
	4 AP 04 Tissue Level of Organization MCQ By OpenStax Start Quiz
	Business Statistics By David Bourgeois Start Quiz

4.5 Combining polynomials using multiplication

Overview

Multiplying a polynomial by a monomial

Distributive property

Multiplying a polynomial by a monomial

Sample set a

Practice set a

Simplifying + ( a + b ) And - ( a + b )

+ ( a + b ) And - ( a + b )

Sample set b

Practice set b

Multiplying a polynomial by a polynomial

Questions & Answers

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Simplifying $+ (a + b)$ And $- (a + b)$

$+ (a + b)$ And $- (a + b)$