Multiplying polynomials

Multiplying polynomials is easy enough, but it can get a bit messy. Especially when dealing with a few variables. But if you know what you are doing, you will manage quite nicely. So let us get down to business.

There is a simple logic behind multiplying polynomials – just multiply every term in the first polynomial with every term of the second polynomial. After that, just tidy up the remaining terms by performing the necessary mathematical operations, such as addition and subtraction. Apart from that, all other rules for multiplication and the order of operations still apply and they should be observed.

Example 1.

So, if you have a polynomial like this:

(4m + 3) * (3m – 2m)

…the first thing you should do is to multiply the terms from the first polynomial with each term in the second one. The process looks like this:

4m*3m + 4m *(-2m) + 3*3m + 3*(-2m)

12m2 – 8m2 + 9m – 6m

After a bit of tidying up, it should look like this:

4m2 + 3m

And that is it. That is the process of multiplying polynomials. It is easy, right? Now we are going to solve a bit more complicated example to show you how to deal with the clutter that appears in these cases.

Example 2.

Let us assume that we have to simplify the product of these polynomials.

(-a + 3b) * (-a2 + ab + 3b2)

Again, we have to start by multiplying each term from the first polynomial with the terms in the second one.

(-a)*(-a2) + (-a)*ab + (-a)*3b2 + 3b2*(-a2) + 3b*ab + 3b*3b2

a3 – a2b – 3ab2 – 3a2b + 3ab2 + 9b3

Now it is time to perform the addition and subtraction to get this mathematical expression in order. Keep in mind that these operations can only be performed with terms whose variables are exactly the same. We will rewrite this expression in a way that these variables are next to each other. So, we get something like this:

a3 – a2b – 3a2b – 3ab2 + 3ab2 + 9b3

We can leave out the two terms that have the same value, but opposite signs since their sum is 0. That means the result of our simplification is:

a3 – 4a2b + 9b3

As you can see, even the most complicated examples are not that difficult to solve as viagra safe. However, a considerable amount of concentration is required because mistakes can happen pretty easily. When you deal with multiplying polynomials, be sure to check your calculations before going further with an assignment. It is worth the extra effort.

So, this is all there is to multiplying polynomials. They can get more complicated by adding more variables or extra polynomials, but if you follow these basic rules and focus on your calculations, you can solve them all. If you wish to practice multiplying polynomials, feel free to use the worksheets below.

Multiplying polynomials exams for teachers

Exam Name File Size Downloads Upload date
Single variable – Integers
Multiplication of polynomials – Integers with a single variable – very easy 557.8 kB 4886 September 3, 2019
Multiplication of polynomials – Integers with a single variable – easy 556.4 kB 3434 September 3, 2019
Multiplication of polynomials – Integers with a single variable – medium 580.7 kB 4845 September 3, 2019
Multiplication of polynomials – Integers with a single variable – hard 567.1 kB 4188 September 3, 2019
Multiplication of polynomials – Integers with a single variable – very hard 589.3 kB 4659 September 3, 2019
Single variable – Decimals
Multiplication of polynomials – Decimals with a single variable – very easy 570.4 kB 2079 September 3, 2019
Multiplication of polynomials – Decimals with a single variable – easy 573.5 kB 1856 September 3, 2019
Multiplication of polynomials – Decimals with a single variable – medium 610.6 kB 2233 September 3, 2019
Multiplication of polynomials – Decimals with a single variable – hard 600.3 kB 2055 September 3, 2019
Multiplication of polynomials – Decimals with a single variable – very hard 642.1 kB 2039 September 3, 2019
Single variable – Fractions
Multiplication of polynomials – Fractions with a single variable – very easy 579.5 kB 2350 September 3, 2019
Multiplication of polynomials – Fractions with a single variable – easy 587.8 kB 2211 September 3, 2019
Multiplication of polynomials – Fractions with a single variable – medium 626.1 kB 2157 September 3, 2019
Multiplication of polynomials – Fractions with a single variable – hard 633.1 kB 2254 September 3, 2019
Multiplication of polynomials – Fractions with a single variable – very hard 680.5 kB 2001 September 3, 2019
Two variables – Integers
Multiplication of polynomials – Integers with two variables – very easy 560 kB 3080 September 3, 2019
Multiplication of polynomials – Integers with two variables – easy 559.8 kB 2470 September 3, 2019
Multiplication of polynomials – Integers with two variables – medium 593.7 kB 3448 September 3, 2019
Multiplication of polynomials – Integers with two variables – hard 583.5 kB 2874 September 3, 2019
Multiplication of polynomials – Integers with two variables – very hard 618.7 kB 2902 September 3, 2019
Two variables – Decimals
Multiplication of polynomials – Decimals with two variables – very easy 582.8 kB 1971 September 3, 2019
Multiplication of polynomials – Decimals with two variables – easy 581 kB 2012 September 3, 2019
Multiplication of polynomials – Decimals with two variables – medium 625.3 kB 1713 September 3, 2019
Multiplication of polynomials – Decimals with two variables – hard 624.3 kB 2229 September 3, 2019
Multiplication of polynomials – Decimals with two variables – very hard 670.5 kB 1987 September 3, 2019
Two variables – Fractions
Multiplication of polynomials – Fractions with two variables – very easy 591 kB 1941 September 3, 2019
Multiplication of polynomials – Fractions with two variables – easy 599.3 kB 1688 September 3, 2019
Multiplication of polynomials – Fractions with two variables – medium 643.3 kB 1872 September 3, 2019
Multiplication of polynomials – Fractions with two variables – hard 640.9 kB 1847 September 3, 2019
Multiplication of polynomials – Fractions with two variables – very hard 689.5 kB 2257 September 3, 2019

Multiplying polynomials worksheets for students

Worksheet Name File Size Downloads Upload date
Single variable – Integers
Integers – Simplify product of monomials and binomials 140.3 kB 3947 September 3, 2019
Integers – Simplify product of monomials and trinomials 199.7 kB 3039 September 3, 2019
Integers – Simplify product of binomials 176.1 kB 4511 September 3, 2019
Integers – Simplify product of binomials and trinomials 260.4 kB 4110 September 3, 2019
Single variable – Decimals
Decimals – Simplify product of monomials and binomials 148.8 kB 2113 September 3, 2019
Decimals – Simplify product of monomials and trinomials 213.1 kB 2009 September 3, 2019
Decimals – Simplify product of binomials 188.2 kB 2092 September 3, 2019
Decimals – Simplify product of binomials and trinomials 275.5 kB 1879 September 3, 2019
Single variable – Fractions
Fractions – Simplify product of monomials and binomials 274.9 kB 2027 September 3, 2019
Fractions – Simplify product of monomials and trinomials 397.9 kB 1796 September 3, 2019
Fractions – Simplify product of binomials 372.3 kB 2136 September 3, 2019
Fractions – Simplify product of binomials and trinomials 2.2 MB 2020 September 3, 2019
Two variables – Integers
Integers – Simplify product of monomials and binomials 167.8 kB 4150 September 3, 2019
Integers – Simplify product of monomials and trinomials 257.7 kB 4535 September 3, 2019
Integers – Simplify product of binomials 241 kB 5722 September 3, 2019
Integers – Simplify product of binomials and trinomials 327.8 kB 6191 September 3, 2019
Single variable – Decimals
Decimals – Simplify product of monomials and binomials 179.2 kB 2001 September 3, 2019
Decimals – Simplify product of monomials and trinomials 269.3 kB 2056 September 3, 2019
Decimals – Simplify product of binomials 252.8 kB 1964 September 3, 2019
Decimals – Simplify product of binomials and trinomials 346.3 kB 1645 September 3, 2019
Single variable – Fractions
Fractions – Simplify product of monomials and binomials 337.2 kB 2068 September 3, 2019
Fractions – Simplify product of monomials and trinomials 483.9 kB 2036 September 3, 2019
Fractions – Simplify product of binomials 446 kB 2005 September 3, 2019
Fractions – Simplify product of binomials and trinomials 817.7 kB 2119 September 3, 2019