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 4990 September 3, 2019
Multiplication of polynomials – Integers with a single variable – easy 556.4 kB 3537 September 3, 2019
Multiplication of polynomials – Integers with a single variable – medium 580.7 kB 4947 September 3, 2019
Multiplication of polynomials – Integers with a single variable – hard 567.1 kB 4291 September 3, 2019
Multiplication of polynomials – Integers with a single variable – very hard 589.3 kB 4774 September 3, 2019
Single variable – Decimals
Multiplication of polynomials – Decimals with a single variable – very easy 570.4 kB 2170 September 3, 2019
Multiplication of polynomials – Decimals with a single variable – easy 573.5 kB 1970 September 3, 2019
Multiplication of polynomials – Decimals with a single variable – medium 610.6 kB 2321 September 3, 2019
Multiplication of polynomials – Decimals with a single variable – hard 600.3 kB 2177 September 3, 2019
Multiplication of polynomials – Decimals with a single variable – very hard 642.1 kB 2160 September 3, 2019
Single variable – Fractions
Multiplication of polynomials – Fractions with a single variable – very easy 579.5 kB 2451 September 3, 2019
Multiplication of polynomials – Fractions with a single variable – easy 587.8 kB 2301 September 3, 2019
Multiplication of polynomials – Fractions with a single variable – medium 626.1 kB 2249 September 3, 2019
Multiplication of polynomials – Fractions with a single variable – hard 633.1 kB 2345 September 3, 2019
Multiplication of polynomials – Fractions with a single variable – very hard 680.5 kB 2091 September 3, 2019
Two variables – Integers
Multiplication of polynomials – Integers with two variables – very easy 560 kB 3158 September 3, 2019
Multiplication of polynomials – Integers with two variables – easy 559.8 kB 2566 September 3, 2019
Multiplication of polynomials – Integers with two variables – medium 593.7 kB 3539 September 3, 2019
Multiplication of polynomials – Integers with two variables – hard 583.5 kB 2976 September 3, 2019
Multiplication of polynomials – Integers with two variables – very hard 618.7 kB 2999 September 3, 2019
Two variables – Decimals
Multiplication of polynomials – Decimals with two variables – very easy 582.8 kB 2052 September 3, 2019
Multiplication of polynomials – Decimals with two variables – easy 581 kB 2103 September 3, 2019
Multiplication of polynomials – Decimals with two variables – medium 625.3 kB 1805 September 3, 2019
Multiplication of polynomials – Decimals with two variables – hard 624.3 kB 2322 September 3, 2019
Multiplication of polynomials – Decimals with two variables – very hard 670.5 kB 2076 September 3, 2019
Two variables – Fractions
Multiplication of polynomials – Fractions with two variables – very easy 591 kB 2026 September 3, 2019
Multiplication of polynomials – Fractions with two variables – easy 599.3 kB 1765 September 3, 2019
Multiplication of polynomials – Fractions with two variables – medium 643.3 kB 1960 September 3, 2019
Multiplication of polynomials – Fractions with two variables – hard 640.9 kB 1928 September 3, 2019
Multiplication of polynomials – Fractions with two variables – very hard 689.5 kB 2358 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 4061 September 3, 2019
Integers – Simplify product of monomials and trinomials 199.7 kB 3214 September 3, 2019
Integers – Simplify product of binomials 176.1 kB 4693 September 3, 2019
Integers – Simplify product of binomials and trinomials 260.4 kB 4248 September 3, 2019
Single variable – Decimals
Decimals – Simplify product of monomials and binomials 148.8 kB 2200 September 3, 2019
Decimals – Simplify product of monomials and trinomials 213.1 kB 2110 September 3, 2019
Decimals – Simplify product of binomials 188.2 kB 2187 September 3, 2019
Decimals – Simplify product of binomials and trinomials 275.5 kB 1978 September 3, 2019
Single variable – Fractions
Fractions – Simplify product of monomials and binomials 274.9 kB 2117 September 3, 2019
Fractions – Simplify product of monomials and trinomials 397.9 kB 1879 September 3, 2019
Fractions – Simplify product of binomials 372.3 kB 2225 September 3, 2019
Fractions – Simplify product of binomials and trinomials 2.2 MB 2131 September 3, 2019
Two variables – Integers
Integers – Simplify product of monomials and binomials 167.8 kB 4397 September 3, 2019
Integers – Simplify product of monomials and trinomials 257.7 kB 4758 September 3, 2019
Integers – Simplify product of binomials 241 kB 5901 September 3, 2019
Integers – Simplify product of binomials and trinomials 327.8 kB 6465 September 3, 2019
Single variable – Decimals
Decimals – Simplify product of monomials and binomials 179.2 kB 2084 September 3, 2019
Decimals – Simplify product of monomials and trinomials 269.3 kB 2134 September 3, 2019
Decimals – Simplify product of binomials 252.8 kB 2055 September 3, 2019
Decimals – Simplify product of binomials and trinomials 346.3 kB 1731 September 3, 2019
Single variable – Fractions
Fractions – Simplify product of monomials and binomials 337.2 kB 2156 September 3, 2019
Fractions – Simplify product of monomials and trinomials 483.9 kB 2139 September 3, 2019
Fractions – Simplify product of binomials 446 kB 2085 September 3, 2019
Fractions – Simplify product of binomials and trinomials 817.7 kB 2215 September 3, 2019