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

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?

Aislinn Reply

tijani

what is titration

John Reply

what is physics

Siyaka Reply

A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance

Jude Reply

Can you compute that for me. Ty

Jude

what is the dimension formula of energy?

David Reply

what is viscosity?

David

what is inorganic

emma Reply

what is chemistry

Youesf Reply

what is inorganic

emma

Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes

Adjei

please, I'm a physics student and I need help in physics

Adjanou

chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.

Pedro

A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity

Krampah Reply

2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.

Sahid Reply

you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s

Samuel Reply

can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?

Joseph Reply

Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time

Joseph

Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing

Joseph

"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true

Ryan

what's motion

Maurice Reply

what are the types of wave

Maurice

answer

Magreth

progressive wave

Magreth

hello friend how are you

Muhammad Reply

fine, how about you?

Mohammed

Mujahid

A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?

yasuo Reply

Who can show me the full solution in this problem?

Reofrir Reply

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

	3 Sample set a By OpenStax Read Online Course
	1 Overview By OpenStax Read Online Course
	Psychology By OpenStax Read Online Course
©flickr: Gareth	Resume Writing MCQ By Abby Sharp Start Quiz
	Young Economist MCQ Test By Robert Murphy Start Test
	Professional makeup certification Test By Angela January Start Quiz
	1 Business Law MCQ 1 By Maureen Miller Start Exam
	PE Power Enigeering Safety By Gerr Zen Start Quiz
	1 Neuroscience Exam 2004 1 By David Corey Start Exam
©flickr: Miguel	Protozoal and Parasitic Infections By Cath Yu Start Quiz
	Respiratory System Drugs By CB Biern Start Quiz
	27 AP 27 Reproductive System Essay By OpenStax Start Flashcards

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 $- (a + b)$