Multiplying Polynomials - The Basics

Adding Exponents Worksheet - Multiplying Polynomials - The Basics

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Multiplying polynomials is the main piece of the pie called algebra. If you don't know how to multiply the polynomials then you can't solve many problems in algebra, I say more you know about how to multiply polynomials, good you are at algebra.

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Adding Exponents Worksheet

As you have the basic knowledge of polynomials and you know how to add or subtract the straightforward polynomials, the next step is to learn how to multiply the polynomials. If you are reading my first article, then please must take a look at my former articles on polynomials, to good understand the content in this presentation.

Multiplying Monomial by a monomial:

The simplest form of multiplying polynomials is to multiply two monomials. This is the base of multiplying the polynomials and my try is always; clear you on basic concepts first of all.

Now, you already know that monomials are the polynomials with only one term. For example, numbers such as 1, - 1, 2, -2 or 5/8 or -9/12 are all monomials. Also, 2a, - 6xy and so are all monomials.

To multiply two or more monomials, multiply the coefficients and then variables, as shown below:

Multiply 3 and 4.

But a joke! What I think, don't you know this straightforward multiplication?

I know it is a grade two question, but the polynomial multiplication base starts, right in grade two. As you know that 3 x 4 = 12, same way you should know the following

3a * 4 = 12a

I used "*" to show multiply as the "multiply sign x" is same as the changeable "x". So, in time to come presentations I will use the star for multiply stamp to avoid confusion.

Look in the above example, the monomial "3a" is getting multiplied with the monomial "4" the retort is "12a". We got the retort by multiplying the numbers (coefficient 3 and constant 4) and just wrote the only changeable "a" with the product 12. If you understood this step you have mastered one third of the polynomial multiplication skill.

Now, let's multiply monomials "4a" and "3bc". Again the procedure is same; multiply the coefficients 3 and 4 to get 12 and write all the three variables "a", "b" and "c" with it, as shown below:

4a * 3bc = 12abc

Now the inquire arises, what if both the monomials have the same variable?

To show how to multiply two similar variables, I want to characterize the exponent rules. In exponents, if we multiply two exponential terms with same bases then the powers are added. For example, if we want to multiply "a^2" ("a to the power 2) to "a^3", we show the clarification as below:

a^2 * a^3 = a^5

(Due to limitation of the report word processor, I can't show the approved exponent notations)

In other words, to multiply same variables we add the powers (exponents) they have.

Keeping this rule in mind, multiplying two monomials with the same changeable is easy as in the next example;

Multiply "3a" and "4a".

3a * 4a = 12a^2 which is read as 12 and "a squared"

Multiply "3ab" with "4abc".

3ab * 4abc = 12a^2b^2c which is read as 12 and "a squared, b squared, c".

Again don't be confused with the notation "^" which means exponent and the estimate after this notation is power or exponent.

I hope you get new knowledge about Adding Exponents Worksheet. Where you'll be able to put to use in your everyday life. And most of all, your reaction is passed about Adding Exponents Worksheet.