# 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 4766 September 3, 2019 Multiplication of polynomials – Integers with a single variable – easy 556.4 kB 3337 September 3, 2019 Multiplication of polynomials – Integers with a single variable – medium 580.7 kB 4720 September 3, 2019 Multiplication of polynomials – Integers with a single variable – hard 567.1 kB 4079 September 3, 2019 Multiplication of polynomials – Integers with a single variable – very hard 589.3 kB 4541 September 3, 2019 Single variable – Decimals Multiplication of polynomials – Decimals with a single variable – very easy 570.4 kB 1997 September 3, 2019 Multiplication of polynomials – Decimals with a single variable – easy 573.5 kB 1760 September 3, 2019 Multiplication of polynomials – Decimals with a single variable – medium 610.6 kB 2150 September 3, 2019 Multiplication of polynomials – Decimals with a single variable – hard 600.3 kB 1955 September 3, 2019 Multiplication of polynomials – Decimals with a single variable – very hard 642.1 kB 1954 September 3, 2019 Single variable – Fractions Multiplication of polynomials – Fractions with a single variable – very easy 579.5 kB 2264 September 3, 2019 Multiplication of polynomials – Fractions with a single variable – easy 587.8 kB 2128 September 3, 2019 Multiplication of polynomials – Fractions with a single variable – medium 626.1 kB 2058 September 3, 2019 Multiplication of polynomials – Fractions with a single variable – hard 633.1 kB 2172 September 3, 2019 Multiplication of polynomials – Fractions with a single variable – very hard 680.5 kB 1918 September 3, 2019 Two variables – Integers Multiplication of polynomials – Integers with two variables – very easy 560 kB 2977 September 3, 2019 Multiplication of polynomials – Integers with two variables – easy 559.8 kB 2374 September 3, 2019 Multiplication of polynomials – Integers with two variables – medium 593.7 kB 3355 September 3, 2019 Multiplication of polynomials – Integers with two variables – hard 583.5 kB 2789 September 3, 2019 Multiplication of polynomials – Integers with two variables – very hard 618.7 kB 2812 September 3, 2019 Two variables – Decimals Multiplication of polynomials – Decimals with two variables – very easy 582.8 kB 1893 September 3, 2019 Multiplication of polynomials – Decimals with two variables – easy 581 kB 1929 September 3, 2019 Multiplication of polynomials – Decimals with two variables – medium 625.3 kB 1621 September 3, 2019 Multiplication of polynomials – Decimals with two variables – hard 624.3 kB 2145 September 3, 2019 Multiplication of polynomials – Decimals with two variables – very hard 670.5 kB 1901 September 3, 2019 Two variables – Fractions Multiplication of polynomials – Fractions with two variables – very easy 591 kB 1858 September 3, 2019 Multiplication of polynomials – Fractions with two variables – easy 599.3 kB 1610 September 3, 2019 Multiplication of polynomials – Fractions with two variables – medium 643.3 kB 1780 September 3, 2019 Multiplication of polynomials – Fractions with two variables – hard 640.9 kB 1767 September 3, 2019 Multiplication of polynomials – Fractions with two variables – very hard 689.5 kB 2177 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 3818 September 3, 2019 Integers – Simplify product of monomials and trinomials 199.7 kB 2906 September 3, 2019 Integers – Simplify product of binomials 176.1 kB 4367 September 3, 2019 Integers – Simplify product of binomials and trinomials 260.4 kB 3958 September 3, 2019 Single variable – Decimals Decimals – Simplify product of monomials and binomials 148.8 kB 2027 September 3, 2019 Decimals – Simplify product of monomials and trinomials 213.1 kB 1935 September 3, 2019 Decimals – Simplify product of binomials 188.2 kB 2005 September 3, 2019 Decimals – Simplify product of binomials and trinomials 275.5 kB 1798 September 3, 2019 Single variable – Fractions Fractions – Simplify product of monomials and binomials 274.9 kB 1938 September 3, 2019 Fractions – Simplify product of monomials and trinomials 397.9 kB 1711 September 3, 2019 Fractions – Simplify product of binomials 372.3 kB 2059 September 3, 2019 Fractions – Simplify product of binomials and trinomials 2.2 MB 1933 September 3, 2019 Two variables – Integers Integers – Simplify product of monomials and binomials 167.8 kB 3928 September 3, 2019 Integers – Simplify product of monomials and trinomials 257.7 kB 4332 September 3, 2019 Integers – Simplify product of binomials 241 kB 5555 September 3, 2019 Integers – Simplify product of binomials and trinomials 327.8 kB 5971 September 3, 2019 Single variable – Decimals Decimals – Simplify product of monomials and binomials 179.2 kB 1914 September 3, 2019 Decimals – Simplify product of monomials and trinomials 269.3 kB 1980 September 3, 2019 Decimals – Simplify product of binomials 252.8 kB 1883 September 3, 2019 Decimals – Simplify product of binomials and trinomials 346.3 kB 1571 September 3, 2019 Single variable – Fractions Fractions – Simplify product of monomials and binomials 337.2 kB 1993 September 3, 2019 Fractions – Simplify product of monomials and trinomials 483.9 kB 1956 September 3, 2019 Fractions – Simplify product of binomials 446 kB 1929 September 3, 2019 Fractions – Simplify product of binomials and trinomials 817.7 kB 2037 September 3, 2019