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 2907 January 1, 1970
Multiplication of polynomials – Integers with a single variable – easy 0 B 2004 January 1, 1970
Multiplication of polynomials – Integers with a single variable – medium 0 B 2906 January 1, 1970
Multiplication of polynomials – Integers with a single variable – hard 0 B 2420 January 1, 1970
Multiplication of polynomials – Integers with a single variable – very hard 0 B 2927 January 1, 1970
Single variable – Decimals
Multiplication of polynomials – Decimals with a single variable – very easy 0 B 1194 January 1, 1970
Multiplication of polynomials – Decimals with a single variable – easy 0 B 1053 January 1, 1970
Multiplication of polynomials – Decimals with a single variable – medium 0 B 1141 January 1, 1970
Multiplication of polynomials – Decimals with a single variable – hard 0 B 1100 January 1, 1970
Multiplication of polynomials – Decimals with a single variable – very hard 0 B 1095 January 1, 1970
Single variable – Fractions
Multiplication of polynomials – Fractions with a single variable – very easy 0 B 1191 January 1, 1970
Multiplication of polynomials – Fractions with a single variable – easy 0 B 1134 January 1, 1970
Multiplication of polynomials – Fractions with a single variable – medium 0 B 1133 January 1, 1970
Multiplication of polynomials – Fractions with a single variable – hard 0 B 1153 January 1, 1970
Multiplication of polynomials – Fractions with a single variable – very hard 0 B 1078 January 1, 1970
Two variables – Integers
Multiplication of polynomials – Integers with two variables – very easy 0 B 1783 January 1, 1970
Multiplication of polynomials – Integers with two variables – easy 0 B 1445 January 1, 1970
Multiplication of polynomials – Integers with two variables – medium 0 B 2068 January 1, 1970
Multiplication of polynomials – Integers with two variables – hard 0 B 1760 January 1, 1970
Multiplication of polynomials – Integers with two variables – very hard 0 B 1834 January 1, 1970
Two variables – Decimals
Multiplication of polynomials – Decimals with two variables – very easy 0 B 946 January 1, 1970
Multiplication of polynomials – Decimals with two variables – easy 0 B 1007 January 1, 1970
Multiplication of polynomials – Decimals with two variables – medium 0 B 912 January 1, 1970
Multiplication of polynomials – Decimals with two variables – hard 0 B 1338 January 1, 1970
Multiplication of polynomials – Decimals with two variables – very hard 0 B 1087 January 1, 1970
Two variables – Fractions
Multiplication of polynomials – Fractions with two variables – very easy 0 B 1022 January 1, 1970
Multiplication of polynomials – Fractions with two variables – easy 0 B 940 January 1, 1970
Multiplication of polynomials – Fractions with two variables – medium 0 B 963 January 1, 1970
Multiplication of polynomials – Fractions with two variables – hard 0 B 1067 January 1, 1970
Multiplication of polynomials – Fractions with two variables – very hard 0 B 1127 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 2280 January 1, 1970
Integers – Simplify product of monomials and trinomials 0 B 1658 January 1, 1970
Integers – Simplify product of binomials 0 B 2728 January 1, 1970
Integers – Simplify product of binomials and trinomials 0 B 2605 January 1, 1970
Single variable – Decimals
Decimals – Simplify product of monomials and binomials 0 B 1082 January 1, 1970
Decimals – Simplify product of monomials and trinomials 0 B 1100 January 1, 1970
Decimals – Simplify product of binomials 0 B 1083 January 1, 1970
Decimals – Simplify product of binomials and trinomials 0 B 1004 January 1, 1970
Single variable – Fractions
Fractions – Simplify product of monomials and binomials 0 B 1031 January 1, 1970
Fractions – Simplify product of monomials and trinomials 0 B 893 January 1, 1970
Fractions – Simplify product of binomials 0 B 1139 January 1, 1970
Fractions – Simplify product of binomials and trinomials 0 B 1072 January 1, 1970
Two variables – Integers
Integers – Simplify product of monomials and binomials 0 B 2616 January 1, 1970
Integers – Simplify product of monomials and trinomials 0 B 2692 January 1, 1970
Integers – Simplify product of binomials 0 B 4179 January 1, 1970
Integers – Simplify product of binomials and trinomials 0 B 4077 January 1, 1970
Single variable – Decimals
Decimals – Simplify product of monomials and binomials 0 B 1081 January 1, 1970
Decimals – Simplify product of monomials and trinomials 0 B 1240 January 1, 1970
Decimals – Simplify product of binomials 0 B 1128 January 1, 1970
Decimals – Simplify product of binomials and trinomials 0 B 990 January 1, 1970
Single variable – Fractions
Fractions – Simplify product of monomials and binomials 0 B 1213 January 1, 1970
Fractions – Simplify product of monomials and trinomials 0 B 1193 January 1, 1970
Fractions – Simplify product of binomials 0 B 1088 January 1, 1970
Fractions – Simplify product of binomials and trinomials 0 B 1148 January 1, 1970