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 0 B 2576 January 1, 1970
Multiplication of polynomials – Integers with a single variable – easy 0 B 1791 January 1, 1970
Multiplication of polynomials – Integers with a single variable – medium 0 B 2563 January 1, 1970
Multiplication of polynomials – Integers with a single variable – hard 0 B 2152 January 1, 1970
Multiplication of polynomials – Integers with a single variable – very hard 0 B 2581 January 1, 1970
Single variable – Decimals
Multiplication of polynomials – Decimals with a single variable – very easy 0 B 1093 January 1, 1970
Multiplication of polynomials – Decimals with a single variable – easy 0 B 963 January 1, 1970
Multiplication of polynomials – Decimals with a single variable – medium 0 B 1053 January 1, 1970
Multiplication of polynomials – Decimals with a single variable – hard 0 B 1015 January 1, 1970
Multiplication of polynomials – Decimals with a single variable – very hard 0 B 998 January 1, 1970
Single variable – Fractions
Multiplication of polynomials – Fractions with a single variable – very easy 0 B 1096 January 1, 1970
Multiplication of polynomials – Fractions with a single variable – easy 0 B 1043 January 1, 1970
Multiplication of polynomials – Fractions with a single variable – medium 0 B 1021 January 1, 1970
Multiplication of polynomials – Fractions with a single variable – hard 0 B 1048 January 1, 1970
Multiplication of polynomials – Fractions with a single variable – very hard 0 B 985 January 1, 1970
Two variables – Integers
Multiplication of polynomials – Integers with two variables – very easy 0 B 1570 January 1, 1970
Multiplication of polynomials – Integers with two variables – easy 0 B 1320 January 1, 1970
Multiplication of polynomials – Integers with two variables – medium 0 B 1820 January 1, 1970
Multiplication of polynomials – Integers with two variables – hard 0 B 1578 January 1, 1970
Multiplication of polynomials – Integers with two variables – very hard 0 B 1643 January 1, 1970
Two variables – Decimals
Multiplication of polynomials – Decimals with two variables – very easy 0 B 864 January 1, 1970
Multiplication of polynomials – Decimals with two variables – easy 0 B 918 January 1, 1970
Multiplication of polynomials – Decimals with two variables – medium 0 B 819 January 1, 1970
Multiplication of polynomials – Decimals with two variables – hard 0 B 1241 January 1, 1970
Multiplication of polynomials – Decimals with two variables – very hard 0 B 1006 January 1, 1970
Two variables – Fractions
Multiplication of polynomials – Fractions with two variables – very easy 0 B 944 January 1, 1970
Multiplication of polynomials – Fractions with two variables – easy 0 B 872 January 1, 1970
Multiplication of polynomials – Fractions with two variables – medium 0 B 875 January 1, 1970
Multiplication of polynomials – Fractions with two variables – hard 0 B 979 January 1, 1970
Multiplication of polynomials – Fractions with two variables – very hard 0 B 1025 January 1, 1970


Multiplying polynomials worksheets for students

Worksheet Name File Size Downloads Upload date
Single variable – Integers
Integers – Simplify product of monomials and binomials 0 B 2049 January 1, 1970
Integers – Simplify product of monomials and trinomials 0 B 1495 January 1, 1970
Integers – Simplify product of binomials 0 B 2490 January 1, 1970
Integers – Simplify product of binomials and trinomials 0 B 2426 January 1, 1970
Single variable – Decimals
Decimals – Simplify product of monomials and binomials 0 B 999 January 1, 1970
Decimals – Simplify product of monomials and trinomials 0 B 1014 January 1, 1970
Decimals – Simplify product of binomials 0 B 981 January 1, 1970
Decimals – Simplify product of binomials and trinomials 0 B 925 January 1, 1970
Single variable – Fractions
Fractions – Simplify product of monomials and binomials 0 B 940 January 1, 1970
Fractions – Simplify product of monomials and trinomials 0 B 822 January 1, 1970
Fractions – Simplify product of binomials 0 B 1062 January 1, 1970
Fractions – Simplify product of binomials and trinomials 0 B 989 January 1, 1970
Two variables – Integers
Integers – Simplify product of monomials and binomials 0 B 2483 January 1, 1970
Integers – Simplify product of monomials and trinomials 0 B 2500 January 1, 1970
Integers – Simplify product of binomials 0 B 3977 January 1, 1970
Integers – Simplify product of binomials and trinomials 0 B 3929 January 1, 1970
Single variable – Decimals
Decimals – Simplify product of monomials and binomials 0 B 1005 January 1, 1970
Decimals – Simplify product of monomials and trinomials 0 B 1170 January 1, 1970
Decimals – Simplify product of binomials 0 B 1041 January 1, 1970
Decimals – Simplify product of binomials and trinomials 0 B 926 January 1, 1970
Single variable – Fractions
Fractions – Simplify product of monomials and binomials 0 B 1140 January 1, 1970
Fractions – Simplify product of monomials and trinomials 0 B 1105 January 1, 1970
Fractions – Simplify product of binomials 0 B 947 January 1, 1970
Fractions – Simplify product of binomials and trinomials 0 B 1060 January 1, 1970