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Multiplying monomials by polynomials review

We use the distributive property to multiply monomials by polynomials. For example, 2x(3x+7) = 6x^2+14x. This article provides a brief review of the topic and gives you a couple of practice problems to try on your own.
In order to multiply monomials like 6, z, squared by polynomials like 7, z, squared, plus, 3, z, minus, 2, we need to apply the distributive property.

Example

Simplify.
Express your answer as a trinomial.
6, z, squared, left parenthesis, 7, z, squared, plus, 3, z, minus, 2, right parenthesis
This is a distributive property problem. How can we distribute start color #6495ed, 6, z, squared, end color #6495ed to each term inside of the parentheses?
This product is equal to 42, z, start superscript, 4, end superscript, plus, 18, z, cubed, minus, 12, z, squared.
Want to learn more about multiplying monomials by polynomials? Check out this video.

Practice

Problem 1
  • Current
Simplify.
Express your answer as a trinomial.
minus, n, squared, left parenthesis, n, squared, plus, 5, n, plus, 6, right parenthesis

Want more practice? Check out this exercise.

Want to join the conversation?

  • duskpin seedling style avatar for user William Thomas
    When will I ever use this in my life?
    (39 votes)
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    • leaf blue style avatar for user VIKAS BARETHA
      POLYNOMIALS USED IN EVERYDAY LIFE
      POLYNOMIALS USED IN FINANCIAL PLANNING

      Polynomials are applied to problems involving construction or materials planning. A polynomial equation can be used in any 2-D construction situation to plan for the number of materials needed.
      USES OF POLYNOMIALS
      Polynomials are a combination of several terms that can be added, subtracted or multiplied but not divided. They are one of the most basic algebraic operations, and many algebra students may wonder why they need to bother learning about them. While polynomials are in sophisticated applications, they also have many uses in everyday life.

      SUMMARY
      POLYNOMIALS USED IN MODELING
      POLYNOMIALS USED IN CONSTRUCTION OR MATERIALS PLANNING

      Some Other Uses
      For people who work in industries that deal with physical phenomena or modeling situations for the future, polynomials come in handy every day. These include everyone from engineers to businessmen.
      USES OF POLYNOMIALS
      Polynomials can also be used to model different situations, like in the stock market to see how prices will vary over time. Business people also use polynomials to model markets, as in to see how raising the price of goods will affect its sales.
      POLYNOMIALS USED IN EXPENSE BUDGETING
      USES OF POLYNOMIALS

      INTRODUCTION

      POLYNOMIALS USED IN PHYSICS
      POLYNOMIALS USED IN INDUSTRY

      Hence, from the following, we observe that polynomials have various uses. People use polynomials in their everyday life. People use polynomials for modeling of various buildings and objects, used in industries, used in construction. They are even used in marketing, finance, stocks .etc. Polynomials are even used in various fields of science, such as physics, where we measure acceleration, or to express units of energy, inertia, or even in electricity .etc. In chemistry, polynomials are used in writing down the chemical equations .etc.

      Polynomials are of great use to every person around.

      Polynomials also are used in scientific problems, including gravitational acceleration problems. The polynomial equation needs to include the object's initial position, which is its distance from Earth's center, its initial velocity and its acceleration due to gravity, which is a constant figure. The accepted standard acceleration due to gravity is 32.17 feet per second squared. That is a basic formula, and many other aspects such as air resistance or air density are factored in by a scientist seeking a highly specific solution.
      Polynomials can be used in financial planning. For instance, a polynomial equation can be used to figure the amount of interest that will accrue for an initial deposit amount in an investment or savings account at a given interest rate.
      POLYNOMIALS ARE USED FOR VARIOUS PURPOSES IN LIFE. POLYNOMIALS ARE USED IN MODELLING, PHYSICS, INDUSTRIES, FINANCE, CONSTRUCTION, GRAVITATION, CHEMISTRY .etc.*

      *USES OF POLYNOMIALS

      Polynomials are useful when it comes to budgeting or expense planning. When you need to earn a given amount of money within a certain time period, polynomials can help you determine the exact amount of time you need to earn that amount. By predicting your expenses and knowing your rate of income, you easily can determine the amount of time you need to work.
      Polynomials come up often in chemistry. Gas equations relating diagnostic parameters can usually be written as polynomials, such as the ideal gas law: PV=nRT (where n is mole count and R is a proportionality constant).

      Formulas of molecules in concentration at equilibrium also can be written as polynomials.

      Polynomials Used In Electronics
      Electronics use many polynomials. The definition of resistance, V=IR, is a polynomial relating the resistance from a resistor to the current through it and the potential drop across it.

      POLYNOMIALS USED IN EVERYDAY LIFE
      Polynomials used in Chemistry
      USES OF POLYNOMIALS
      Polynomials are used in physics to describe the trajectory of projectiles. Polynomial integrals (the sums of many polynomials) can be used to express energy, inertia and voltage difference, to name a few applications.
      POLYNOMIALS USED IN GRAVITATIONAL ACCELERATION
      *https://prezi.com/yipjmwht42a5/polynomials-used-in-everyday-life/*
      (82 votes)
  • old spice man green style avatar for user Benjamin Banner
    What are some examples of where one would multiply binomials in everyday life?
    (30 votes)
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  • blobby green style avatar for user Hurias
    why do we do a lot steps, when we can use distributive property to solve it?
    (4 votes)
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  • boggle green style avatar for user David Wang
    Why would you want to expand it if you could leave it in it's simplified form?
    (5 votes)
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  • piceratops tree style avatar for user GodSlayer
    I don't know why but this seems a piece of cake to me
    (7 votes)
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  • blobby green style avatar for user torresa07140
    wow i got it right but said i got it wrong lmao
    (3 votes)
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  • blobby green style avatar for user Foster Jr., Michael
    What are some examples of where one would multiply binomials in everyday life?
    (1 vote)
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  • aqualine ultimate style avatar for user piperbanys
    If you had a problem like this: x(x−3)(x+3), would you multiply (x−3)(x+3) first or distribute the x and then multiply? If you distribute the x first, do you distribute it over (x−3) or (x−3) and (x+3)?
    (2 votes)
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    • stelly blue style avatar for user Kim Seidel
      You can do either approach. Remember, commutative property of multiplication tells us that we can multiply in any order. If you multiply 2*3*5, you can do (2*3) then times 5, or you can do (3*5) then multiply with the 2. Both give you the answer of 30.

      If you distribute the "x" first, you multiply it with just one binomial. x(x-3) = (x^2-3x). Then, you multiply the new binomial with the remaining one: (x^2-3x)(x+3)

      Hope this helps.
      (5 votes)
  • female robot ada style avatar for user MICHAEL STOKES
    I know a lot of people ask and a lot of people answer but I still have to ask. How will this ever come in handy in every day life? I can guarantee that no one can find a logical answer
    (0 votes)
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  • blobby green style avatar for user Sabina Day
    Will they have these problems on the ACT?
    (2 votes)
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