# 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 4411 September 3, 2019 Multiplication of polynomials – Integers with a single variable – easy 556.4 kB 3065 September 3, 2019 Multiplication of polynomials – Integers with a single variable – medium 580.7 kB 4367 September 3, 2019 Multiplication of polynomials – Integers with a single variable – hard 567.1 kB 3789 September 3, 2019 Multiplication of polynomials – Integers with a single variable – very hard 589.3 kB 4232 September 3, 2019 Single variable – Decimals Multiplication of polynomials – Decimals with a single variable – very easy 570.4 kB 1797 September 3, 2019 Multiplication of polynomials – Decimals with a single variable – easy 573.5 kB 1563 September 3, 2019 Multiplication of polynomials – Decimals with a single variable – medium 610.6 kB 1944 September 3, 2019 Multiplication of polynomials – Decimals with a single variable – hard 600.3 kB 1764 September 3, 2019 Multiplication of polynomials – Decimals with a single variable – very hard 642.1 kB 1765 September 3, 2019 Single variable – Fractions Multiplication of polynomials – Fractions with a single variable – very easy 579.5 kB 2055 September 3, 2019 Multiplication of polynomials – Fractions with a single variable – easy 587.8 kB 1917 September 3, 2019 Multiplication of polynomials – Fractions with a single variable – medium 626.1 kB 1844 September 3, 2019 Multiplication of polynomials – Fractions with a single variable – hard 633.1 kB 1973 September 3, 2019 Multiplication of polynomials – Fractions with a single variable – very hard 680.5 kB 1737 September 3, 2019 Two variables – Integers Multiplication of polynomials – Integers with two variables – very easy 560 kB 2738 September 3, 2019 Multiplication of polynomials – Integers with two variables – easy 559.8 kB 2190 September 3, 2019 Multiplication of polynomials – Integers with two variables – medium 593.7 kB 3114 September 3, 2019 Multiplication of polynomials – Integers with two variables – hard 583.5 kB 2572 September 3, 2019 Multiplication of polynomials – Integers with two variables – very hard 618.7 kB 2578 September 3, 2019 Two variables – Decimals Multiplication of polynomials – Decimals with two variables – very easy 582.8 kB 1706 September 3, 2019 Multiplication of polynomials – Decimals with two variables – easy 581 kB 1746 September 3, 2019 Multiplication of polynomials – Decimals with two variables – medium 625.3 kB 1405 September 3, 2019 Multiplication of polynomials – Decimals with two variables – hard 624.3 kB 1976 September 3, 2019 Multiplication of polynomials – Decimals with two variables – very hard 670.5 kB 1737 September 3, 2019 Two variables – Fractions Multiplication of polynomials – Fractions with two variables – very easy 591 kB 1664 September 3, 2019 Multiplication of polynomials – Fractions with two variables – easy 599.3 kB 1415 September 3, 2019 Multiplication of polynomials – Fractions with two variables – medium 643.3 kB 1609 September 3, 2019 Multiplication of polynomials – Fractions with two variables – hard 640.9 kB 1563 September 3, 2019 Multiplication of polynomials – Fractions with two variables – very hard 689.5 kB 1980 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 3483 September 3, 2019 Integers – Simplify product of monomials and trinomials 199.7 kB 2631 September 3, 2019 Integers – Simplify product of binomials 176.1 kB 4046 September 3, 2019 Integers – Simplify product of binomials and trinomials 260.4 kB 3556 September 3, 2019 Single variable – Decimals Decimals – Simplify product of monomials and binomials 148.8 kB 1838 September 3, 2019 Decimals – Simplify product of monomials and trinomials 213.1 kB 1751 September 3, 2019 Decimals – Simplify product of binomials 188.2 kB 1793 September 3, 2019 Decimals – Simplify product of binomials and trinomials 275.5 kB 1598 September 3, 2019 Single variable – Fractions Fractions – Simplify product of monomials and binomials 274.9 kB 1746 September 3, 2019 Fractions – Simplify product of monomials and trinomials 397.9 kB 1535 September 3, 2019 Fractions – Simplify product of binomials 372.3 kB 1870 September 3, 2019 Fractions – Simplify product of binomials and trinomials 2.2 MB 1748 September 3, 2019 Two variables – Integers Integers – Simplify product of monomials and binomials 167.8 kB 3491 September 3, 2019 Integers – Simplify product of monomials and trinomials 257.7 kB 3942 September 3, 2019 Integers – Simplify product of binomials 241 kB 5195 September 3, 2019 Integers – Simplify product of binomials and trinomials 327.8 kB 5417 September 3, 2019 Single variable – Decimals Decimals – Simplify product of monomials and binomials 179.2 kB 1723 September 3, 2019 Decimals – Simplify product of monomials and trinomials 269.3 kB 1803 September 3, 2019 Decimals – Simplify product of binomials 252.8 kB 1713 September 3, 2019 Decimals – Simplify product of binomials and trinomials 346.3 kB 1405 September 3, 2019 Single variable – Fractions Fractions – Simplify product of monomials and binomials 337.2 kB 1806 September 3, 2019 Fractions – Simplify product of monomials and trinomials 483.9 kB 1777 September 3, 2019 Fractions – Simplify product of binomials 446 kB 1748 September 3, 2019 Fractions – Simplify product of binomials and trinomials 817.7 kB 1817 September 3, 2019