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 3121 January 1, 1970
Multiplication of polynomials – Integers with a single variable – easy 0 B 2152 January 1, 1970
Multiplication of polynomials – Integers with a single variable – medium 0 B 3109 January 1, 1970
Multiplication of polynomials – Integers with a single variable – hard 0 B 2620 January 1, 1970
Multiplication of polynomials – Integers with a single variable – very hard 0 B 3161 January 1, 1970
Single variable – Decimals
Multiplication of polynomials – Decimals with a single variable – very easy 0 B 1266 January 1, 1970
Multiplication of polynomials – Decimals with a single variable – easy 0 B 1100 January 1, 1970
Multiplication of polynomials – Decimals with a single variable – medium 0 B 1198 January 1, 1970
Multiplication of polynomials – Decimals with a single variable – hard 0 B 1154 January 1, 1970
Multiplication of polynomials – Decimals with a single variable – very hard 0 B 1158 January 1, 1970
Single variable – Fractions
Multiplication of polynomials – Fractions with a single variable – very easy 0 B 1261 January 1, 1970
Multiplication of polynomials – Fractions with a single variable – easy 0 B 1193 January 1, 1970
Multiplication of polynomials – Fractions with a single variable – medium 0 B 1192 January 1, 1970
Multiplication of polynomials – Fractions with a single variable – hard 0 B 1220 January 1, 1970
Multiplication of polynomials – Fractions with a single variable – very hard 0 B 1146 January 1, 1970
Two variables – Integers
Multiplication of polynomials – Integers with two variables – very easy 0 B 1896 January 1, 1970
Multiplication of polynomials – Integers with two variables – easy 0 B 1515 January 1, 1970
Multiplication of polynomials – Integers with two variables – medium 0 B 2201 January 1, 1970
Multiplication of polynomials – Integers with two variables – hard 0 B 1861 January 1, 1970
Multiplication of polynomials – Integers with two variables – very hard 0 B 1943 January 1, 1970
Two variables – Decimals
Multiplication of polynomials – Decimals with two variables – very easy 0 B 992 January 1, 1970
Multiplication of polynomials – Decimals with two variables – easy 0 B 1062 January 1, 1970
Multiplication of polynomials – Decimals with two variables – medium 0 B 968 January 1, 1970
Multiplication of polynomials – Decimals with two variables – hard 0 B 1397 January 1, 1970
Multiplication of polynomials – Decimals with two variables – very hard 0 B 1145 January 1, 1970
Two variables – Fractions
Multiplication of polynomials – Fractions with two variables – very easy 0 B 1082 January 1, 1970
Multiplication of polynomials – Fractions with two variables – easy 0 B 997 January 1, 1970
Multiplication of polynomials – Fractions with two variables – medium 0 B 1023 January 1, 1970
Multiplication of polynomials – Fractions with two variables – hard 0 B 1123 January 1, 1970
Multiplication of polynomials – Fractions with two variables – very hard 0 B 1199 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 2420 January 1, 1970
Integers – Simplify product of monomials and trinomials 0 B 1788 January 1, 1970
Integers – Simplify product of binomials 0 B 2895 January 1, 1970
Integers – Simplify product of binomials and trinomials 0 B 2717 January 1, 1970
Single variable – Decimals
Decimals – Simplify product of monomials and binomials 0 B 1143 January 1, 1970
Decimals – Simplify product of monomials and trinomials 0 B 1159 January 1, 1970
Decimals – Simplify product of binomials 0 B 1136 January 1, 1970
Decimals – Simplify product of binomials and trinomials 0 B 1069 January 1, 1970
Single variable – Fractions
Fractions – Simplify product of monomials and binomials 0 B 1102 January 1, 1970
Fractions – Simplify product of monomials and trinomials 0 B 946 January 1, 1970
Fractions – Simplify product of binomials 0 B 1202 January 1, 1970
Fractions – Simplify product of binomials and trinomials 0 B 1132 January 1, 1970
Two variables – Integers
Integers – Simplify product of monomials and binomials 0 B 2688 January 1, 1970
Integers – Simplify product of monomials and trinomials 0 B 2791 January 1, 1970
Integers – Simplify product of binomials 0 B 4289 January 1, 1970
Integers – Simplify product of binomials and trinomials 0 B 4276 January 1, 1970
Single variable – Decimals
Decimals – Simplify product of monomials and binomials 0 B 1126 January 1, 1970
Decimals – Simplify product of monomials and trinomials 0 B 1277 January 1, 1970
Decimals – Simplify product of binomials 0 B 1169 January 1, 1970
Decimals – Simplify product of binomials and trinomials 0 B 1036 January 1, 1970
Single variable – Fractions
Fractions – Simplify product of monomials and binomials 0 B 1267 January 1, 1970
Fractions – Simplify product of monomials and trinomials 0 B 1240 January 1, 1970
Fractions – Simplify product of binomials 0 B 1167 January 1, 1970
Fractions – Simplify product of binomials and trinomials 0 B 1206 January 1, 1970