Multiplication of Polynomials
We have now come to the end of week 5 which is our last week of hybrid classes. Starting next week we are going to become a cohort class. This week we started a new unit which was all about polynomials. The part that I thought was the most important was the multiplication of polynomials. We learned a few different methods and I believe this skill can be applied to many equations as polynomials are very important part of math. In addition to this, the multiplication of polynomials comes up in many questions.
There are a few different methods to deal with problems that involve multiplying polynomials, I personally like to use the distributive property rule as I find it the simplest way to get the answer.
The first example we are going to be working with is multiplying a binomial by a binomial. Here is the sample question:
Step 1 – using the distributive property: multiplying two binomials looks a little different then what we learned back in grade 9 where we would multiply one term outside the brackets by anything in the brackets. This question might look a little more difficult but it’s still the same idea. All you need to do is multiply each term in the first set of brackets by each term in the second set of brackets. To make it even easier for yourself you can write out two separate equations and then distribute one term into the brackets.
Step 2 – solving the equation: now the question looks very simple, just like the questions that we have previously done in grade 9. All that needs to be done is multiply “4a” by everything in the brackets in front of it and multiply “9b” by everything in the brackets in front of it. Also remember to add the exponents of the variables that are being multiplied together (variables with no exponent have an exponent of 1).
Step 3 – collecting like terms: now that we have distributed all our terms and multiplied we need to collect the like terms. Like terms are the terms that have the same variable AND same exponent. Terms with the same variable but different exponents are not like terms. When collecting like terms you are adding polynomials, so the coefficients (number in front of the letter – the variable) are the only things that change, the variables stay the same. After this done you will be left with the final answer and the question is complete.
Example 2: We are now going to look at an example which is similar to what we did previously except this time we will be multiplying a binomial by a trinomial.
Here is the sample question we are going to be working with:
Step 1 – using the distributive property: since this question has a trinomial in it, it may look more difficult. However, the process is almost exactly the same, it is just a little bit longer. Before you needed to multiply the terms in the first bracket by the other two terms, now you need to multiply them by the other three terms. This is very similar it just adds a few terms. Once again, to make it easier for yourself you can write out two separate equations and distribute only one term into the brackets.
Step 2 – solving the equation: now we have a much simpler looking equation, a few more terms compared to the previous question but still the same idea is involved. Now all that needs to be done is multiply “
Step 3 – collecting like terms: now that we have distributed all our terms and multiplied we need to collect the like terms. Like terms are the terms that have the same variable AND same exponent. Terms with the same variable but different exponents are not like terms. When collecting like terms you are adding polynomials, so the coefficients (number in front of the letter – the variable) are the only things that change, the variables stay the same. After this done you will be left with the final answer and the question is complete.
Summary:
We have now gone through two examples of multiplying polynomials and as you can see questions with more terms are really not much harder they just require you to repeat the process more times. I think that this skill is very useful and can be applied in many different questions. It is very important to know how to deal with polynomials, especially multiplying them since this is a very common question you may come across. I used the distributive property in these questions but there are other strategies that may be applied. The key is to find a strategy that works for you.