Software for Geometric Learning

Software for Geomtric Learning

Software for Geomtric Learning - May, when we learn in math sometimes difficult understand about geometry. Then we need a way to be more easyly. With this software we can to be more easly understand about geometry. In this software includes a lot of features. In this software we can know where is location of the point, we can draw tangent to circle, can easily draw a circle, etc.

The software name is GeoGebra. Geogebra name comes from geometry and algebra. To download this software you can click here.

Some screen shoot from maticschool :

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Download GeoGebra 4.2.6

Download GeoGebra 4.2.6

Download GeoGebra 4.2.6 - This software will help you when you learn math. Especially when you learn about algebra and geometry. Plus this software is open source. Then this software can used in a variety of operating systems. The operating systems is windows, mac, ubuntu, debian, and other linux, java webstar, android and etc. Next this software do not need a good computer.

This is a some screen schoot from maticschool :

To download you can click here

For windows : size         : 29 mb
                      extension : .exe
                      password : no password

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Multiplication in Algebra ( part 3 )

Multiplication in Algebra | Difference of Two Squares

Multiplication in Algebra - Difference of Two Squares - Still the same as previous aljbar multiplication, this multiplication also still use the distributive properties. Now we will discuss the binomial multiplication of (x + y) and (x - y). Now you see this picture below :

From the picture we can draw conclusions :

( x + y ) ( x – y )  =  x ( x – y ) + y ( x – y )

                           = ((x . x) – ( x . y)) + ((y . x ) – ( y . y ) )

                           =     x²     – xy  + yx  - y²     =      x² + y²

Example : 

( 2x + 3y ) ( x - 2y ) = 2x ( x - 2y ) + 3y ( x - 2y )

                                = (( 2x . x) -  ( 2x . 2y )) + (( 3y . x ) - ( 3y . 2y ) )

                                = ( 2x2        - ( 2 . 2 x . y )) + ( 3yx   -  ( 3 . 2 . y . y )

                                = 2x2   - 4xy   +   3yx   - 6y2 

                                = 2x2       - 1xy      - 6y2

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Multiplication in Algebra ( part 2 )

Multiplication in Algebra | Binomial multiplication with two tribes

Multiplication in Algebra - Binomial multiplication with two tribes - 
   Still the same as the previous multiplication. Binomial multiplication with two tribes still use the distributive properties.What is the nature of the distributive ? You can click here for know about distributive. Binomial multiplication with two tribes you can see this picture below :

    From the picture we can draw conclusions :

( a + b ) ( c + d ) = ( a x c ) + ( a x d ) + (b x c ) + ( b x d )

                           =       ac    +     ad       +   bc      +    bd 

   Example : 

( 2x + 3y ) ( x + 2 y ) = ( 2x . x ) + ( 2x . 2y ) + ( 3y . x ) + ( 3y . 2y)

                                  = 2x2    + ( 2 . 2 . x . y ) + 3yx       + ( 3 . 2 . y . y )

                                  = 2x2    +       4xy          + 3xy       + 6y2

                                             = 2x2     +                   6xy              + 6y2 


                                                                                                                                                               next part ( to part 3 )

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Multiplication in the Algebra ( part 1 )

Multiplication in the Algebra | 

The Multiplication Rate With Two or More Parts 

Multiplication in the Algebra - The Multiplication Rate With Two or More Parts -

The rate of multiplication algebra we will use as the basis of distributive properties. To know what was the nature of distributive, you can click here.

The Multiplication Rate With Two or More Parts 

        

         We can use the nature of distributive for the multiplication rate with two or more parts. 

    Distributive Properties : 

      a x ( b + c ) = ( a x b ) + ( a x c ) or ( a + b ) x c = ( a x c ) + ( b + c )

    Distributive Properties in the algebra : 

       aX x ( 1X + 1y ) = (aX x 1X ) + ( aX x 1y)

                                  = 1aX²   + 1aXy

         Example :

                a. 1a ( 3a + 4b) = ( 1a x 3a ) + ( 1a x 4b )

                                         = ( 1 x a x 3 x a ) + ( 1 x a x 4 x b )

                                         = ( 1 x 3 x a x a ) + ( 1 x 4 x a x b )

                                         = ( 3 x a² ) + ( 4 x ab)

                                         =  3a²  + 4ab

                                                                                                                                   next part ( to part 2 )

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the Answer

The Answer -  This answer from the exercise here. In this answer will be more explanation details. You can see details answer below :

1. 5x + 3y + 2xy = 5x + 3y + 2xy

2. 3x + 2x = 5x

3. 5x + 2y - 20x + 10y = 5x - 20x + 2y + 10y
                                   = -15x       + 12y

4. xy + x + 2y = 1xy + 1x + 2y = xy + x 2y

5. 9x + 3y + 1x = 9x + 1x + 3y = 10x + 3y

6. -3xy + 2y + 5xy = -3xy + 5xy + 2y 
                            = 2xy + 2y

7. x + y = 1x + 1y = x + y

8. 7xy - 5y + xy = 7xy - 5y + 1xy = 7xy + 1xy - 5y
                         = 8xy - 5y

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Exercises Reduction and Algebraic Addition

Exercises Reduction and Algebraic Addition -  Sometimes we need to learn about the practice. In this post Maticschool will give you some practice questions on algebra.Before you do the more it helps you to read some of our posts about algebra. To see more our post about algebra click here.           






Exercises : 

 1. 5x + 3y + 2xy = 
 2. 3x + 2x = 
 3. 5x + 2y - 20x + 10y =
 4. xy + x + 2y =
 5. 9x + 3y + 1x =
 6. -3xy + 2y + 5xy =
 7. x + y =
 8. 7xy - 5y + xy =

The Answer click here ( coming soon)

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Basics of Algebra

Basics of Algebra - Maybe some people already know about algebra. But there are also people who do not know about it. In this explanation I will make an example :

Consider the following example :

a. 3x
b. 3x + 5xy
c. 4x + 2 + 3xy + 5

From the following example, we can determine which variables, coefficient, constant, and tribes algebra. In the math sentence above, the coefficient is concatenated variable numbers. So the coefficient is 3 in a. example, and then 3 and 5 in the b. example. And the last in c. example is just 4 and 3. Then just 2 and 5 in c. example, continued without any letters is constant. Next variables is the alphabet that follow the number. So from the example the variables is x, y, and xy.How about tribes algebra ? Look back from the three example above. For a. example called single tribe.

Keyword for this post :

basic algebra

algebra

elementary algebra

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Addition or Recudtion in Al-Gebra

Addition or Recudtion in Al-Gebra

Addition or Recudtion in Al-Gebra - Basically arithmetic operations in algebra no different integer arithmetic operations. Arithmetic operations of addition and subtraction algebra tribe done by adding or subtracting the coefficients between similar tribes. For example you can see the example below :

Answer the following question correctly !

1. 2x + 3x =
2. 4x + 5x =
3. 2x + 2y + 2x =
4. 2x + 1y =
Answer

1. 2x + 3x = 5x
2. 4x + 5x = 9x
3. 2x + 2y + 2x = 2x + 2x + 2y = 4x + 2y
4. 2x + 1y = 2x + 1y = 2x + y
Study :

From the example , in fact  is same. But before answer we must look the variable behing the number.  When the variable is same, numbers can be added or subtracted. But when the variable is not same, numbers can not be added or subtracted. So the result like the example 3th and 4th.

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