INFORMATION ON QUADRATIC EXPRESSIONS AND EQUATIONS.

What are quadratic expressions and equations?

Quadratic expression is any expression where the power or degree of the first term is 2. To be able to determine whether an expression is a quadratic expression or not you can see if the highest exponent or degree of the first term is 2. The expression must have a power of 2, No lower and no higher.

The first solution for a quadratic expression was done by mathematician Muhammad ibn Musa al-Khwarizmi. It is said that the quadratic formula covering all cases was first obtained by Simon Stevin in 1594. Rene Descartes published la Geometrie that contains special cases of the quadratic formula in the form we know today back in 1953.

Quadratic expressions are the process of solving quadratic questions containing only a quadratic term, however, a quadratic equation asserts that a quadratic equation is equal to some other expression. 

For example "x^2 + 11x + 24," can be considered a quadratic expression.  

"5x^2 + 6x + 2 = 0" can be considered quadratic equation. 

The General quadratic formula is : ax^(2) + bx + c. 

To be able to solve questions such as those you will first need to know the methods which can be used to do so, some of which are posted in this blog such as Highest common factor, The difference of two squares, and foil method.

Example Question: 

x^2 + 2x - 15 

x^2 + 5x - 3x - 15 

x( x + 5 ) -3 ( x + 5 ) 

(x - 3) (x+5)

As shown above, that solution contains a combination of methods that are used to arrive at our final answer.

The main difference between a quadratic expression and a quadratic equation is the equal sign.

Quadratic expressions and equations can be used in our real world to solve many problems in our day-to-day life such as Programming/coding, calculating areas, determining products' profit, etc.

To learn more in-depth about solving quadratic equations and expressions you can check some of our pages that are posted on this blog. 

LEARN TO FACTORIZE EXPRESSIONS USING THE HIGHEST COMMON FACTOR (HCF) METHOD

What does factorizing with the Highest Common Factor means?

 Factorizing expression is the reverse process of expanding brackets. 

To factor, an expression simply means that you have to : 

1. Put it in brackets by removing the common factors. 

2. Find the highest factor in the given expression.

3. Fill in each term in the bracket by multiplying out.

Factorizing expressions was said to be founded by an ancient Greek mathematicians that proved the fundamental theorem of arithmetic.

Factoring expression can be used in the real world to divide things into equal pieces, understanding time and making calculations during travel, and many more useful things.

Factorizing an expression can be done using two methods; These methods are called: 

Highest Common Factor and Difference of Two squares method.

The HCF method is when you use the "Highest Common Factor" (HCF) to fill in each terms in the bracket by multiplying out.

The Difference of two square methods is when two squares is being subtracted from each other and when factored it can be seen in the foil method format.

If you want to get a more detailed explanation on how to use this method and how to use the other method you can feel free to check out our pages on this blog titled: 

"STEP BY STEP GUIDE ON HOW TO FACTORIZE USING THE HCF METHOD + DIAGRAMS"

AND 

"STEP BY STEP GUIDE ON HOW TO FACTORIZE USING THE DIFFERENCES OF TWO SQUARES METHOD + DIAGRAMS" 

LEARN TO FACTORIZE EXPRESSIONS USING THE DIFFERENCE OF TWO SQUARES

 What is the difference of two squares?

The difference of two squares is an expression that two square is being subtracted from each other and when factored it can be seen in the foil method format.

for example : a^2 - b^2 = (a + b) (a - b)

This method is based on the pattern and can be verified when the parentheses are expanded. 

Historically it is said that the Babylonians were the ones who used the difference of two squares to calculate multiplications.

This method is used in today's world to solve mathematical problems and in other jobs that requires a degree in mathematics.

There are some common mistakes that are often made by students when using this method,

In this blog you will find a page titled:

"LEARN TO FACTORIZE USING THE DIFFERENCES OF TWO SQUARES "

Where you can find the mistakes made and tips on how to reduce them. 

There is also a step-by-step guide that you can read to get a better understanding on the topic.

If you like to learn to factorize using the other method: "Highest common factor method:"

You can always feel free to check out the page titled : 

"LEARN TO FACTORIZE USING HIGHEST COMMON THE FACTOR (HCF)"

 

WHAT IS MEANT BY EXPRESSIONS?

 

What are Expressions?

In mathematics, an expression or mathematical expressions are a combination of symbols, variables, numbers, operations, brackets, functions, and grouping to help determine the order of operations. 

It is said that at the end of the 16th century Francois Viete introduced symbols. These symbols are now called variables today, they are used for representing unknown numbers. This has created a new algebra that consists of computing with symbolic expressions as if they were numbers. 

It is also said that in the 17th century the use of "x" was used in representing unknown variables and, It is said that it was Rene Descartes who was responsible for this development. It's being thought that this was first used in the published form of "La Géométrie"

There are many things you can do with expressions such as: simplifying, expanding, evaluating, and many more...

Expressions can be used in the real world to solve scientific problems, doing carpentry, and even in architectural activities/jobs.

 

In this blog, there is a page containing information on how to solve expressions such as: simplifying and expanding them. What is simplifying and expanding you asked??

Expanding and simplifying expressions is the action of multiplying out the brackets from an expression and then simplifying the resulting expression by collecting the like terms available, there are several types of expanding and simplifying questions which comes with different method in solving them...If you want to learn these methods feel free to check out our pages titled: 

"Fun and easy steps on how to expand and simplify expressions properly + mistakes and tips"

OR

"Diagrams depicting simplifying and expanding expressions with different methods."