Polynomials - The Simplest Form of the Algebraic Expressions

Adding Exponents Worksheet - Polynomials - The Simplest Form of the Algebraic Expressions

Hello everybody. Today, I learned about Adding Exponents Worksheet - Polynomials - The Simplest Form of the Algebraic Expressions. Which could be very helpful to me and also you. Polynomials - The Simplest Form of the Algebraic Expressions

Polynomials are very very foremost to understand to be successful in algebra. As I promised in my previous articles, that we are going to examine algebra by taking two paths. Polynomials are the second path which goes to algebra destination as the first path, equations, we are pursuing already. The foremost note to remember is that the algebraic relations or algebraic expressions give rise to both the polynomials and equations. Also, the word phrases from the daily life give birth to algebraic relations.

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Adding Exponents Worksheet

I can say that the polynomials are a type of algebraic relations. Polynomials involve the whole amount powers of variables. They don't have negative or fractional powers. In other words, it can be said that polynomials are the simplest form of the algebraic expressions.

A polynomial can have one to infinite amount of terms. Also the polynomials can be classified according to the amount of terms they contain. We will discuss the classification of the polynomials in my coming articles in more detail. The objective of this description is to introduce the grade eight or higher students with polynomials.

As the polynomials are the simplest form of the algebraic expressions, they are written without the use of equal sign. When an equal sign is included with a polynomial, then it is called a polynomial equation.

Following are some examples of polynomials;

1. 3c

2. 4x + 2y

3. 2m - n - 9

4. 8

5. 5a+ 3ab - 9

Notice, in example 4, amount "8" is a polynomial which means all the numbers can be called as polynomials. These numbers have the variable with power zero.

In all other examples, the polynomials have variables with exponent one. But remember that, variables can have any whole amount as their exponents (power). Don't be surprised by the polynomials having variables with powers such as, 3, 5, 7 or even higher.

If there is a variable at the lowest (at denominator) in an algebraic relation, that algebraic relation is not a polynomial. For example;

5xy - 3/x - 5

Notice that, 3 has x as its denominator, therefore above relation is not a polynomial. Keep in mind that, the variable at the denominator in a relation or one with a negative power are the same. If you see a negative power of a variable, decimal or fractional power of a variable in an algebraic relation, never ever consider that relation as a polynomial.

Polynomials are very foremost as they are used in calculus, in science, economics and in many other areas. So, stay tuned as more explanations about the polynomial and algebra are on their way.

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Multiplying Polynomials - The Basics

Adding Exponents Worksheet - Multiplying Polynomials - The Basics

Hi friends. Yesterday, I discovered Adding Exponents Worksheet - Multiplying Polynomials - The Basics. Which may be very helpful in my opinion and you. Multiplying Polynomials - The Basics

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.

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