102-Tool to calculate difference between two dates (Age calculator)

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Tool to get the difference between two dates

Now we will learn very useful tools to calculate the difference between two dates in years, months, and days. Now we calculate our age today. It is a very interesting software.

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Simply enter the data in the Start Date and End date fields. Here your start date is smaller than the end date. It becomes very easy to calculate your age in years/Months/days. by using this software. So many times we need to calculate the difference between two dates such as "At what age I completed my Graduation" or "What is the difference between me and my mother". This is a very easy tool to calculate such differences.

 ANIL SATPUTE

101-GRE Math-6-Important Key points and formulas

Click here for the previous basics.

In continuation of part - 5, we will see all the important formulas and useful statements which are to be used in the Math test GRE.

Factorization (Continued):

b) Factorization of Polynomial (Continued): 

4) (x - a) (x - b) = x (x - b) - a (x - b)
                         = x ² - b x - a x + ab
                         = x ² - (a + b) x + ab
Generally, we call x ² as the first term, (a + b) x as the middle term, and ab as the last term. 

Basic concept: 

a) Step-1: See the sign of the last term.
b) Step-2: Here it is "+" so factorize the product of the coefficient of the first term (here it is 1) and the last term in such a way that the SUM of these two factors must be the coefficient of the middle term.
c) Step-3: Get the factors.

Example-1:

Factorize: x ² - 10 x + 21.

a) Step-1: Here sign of the last term 21 is "+"
b) Step-2: The coefficient of the first term is 1 and the last term is 21, so the product of 1 and 21 is 21. Now the factors of 21 are 3 and 7 and as the sign of the last term is "+", their addition is -3 - 7 = -10 which is the coefficient of the middle term.  
                         = x ² - 10 x + 21
                         = x ² - (3 + 7) x + (3 x 7)
                         = x ² - 3 x - 7 x + (3 x 7)
                         = x (x - 3) - 7 (x - 3)
                         = (x - 3) (x - 7)
c) Step-3: So the factors of x ² - 10 x + 21 are (x - 3) and (x - 7) 

Example-2:

Factorize: 8 x ² - 14 x + 5.

a) Step-1: Here sign of the last term 5 is "+"
b) Step-2: The coefficient of the first term is 8 and the last term is 5, so the product of 8 and 5 is 8 X 5. Now the factors of 8 X 5 are 2, 2, 2, and 5 and as the sign of the last term is "+", so, we take two factors in such a way that their sum will be 14. Here 2, 2, 2, and 5 will give us 4 and 10. So, here addition is -4 - 10 = -14 which is the coefficient of the middle term.  
                         = 8 x ² - 14 x + 5
                         = 8 x ² - (4 + 10) x + 5
                         = 8 x ² - 4 x - 10 x + 5
                         = 4 x (2 x - 1) - 5 (2 x - 1)
                         = (4 x - 5) (2 x - 1)
c) Step-3: So the factors of 8 x ² - 14 x + 5 are (2 x - 1) and (4 x - 5).

In the next part, we will see a few examples and some essential formulae.

Click here for the next basics.

ANIL SATPUTE

100-GRE Math-5-Important Key points and formulas

Click here for the previous basics.

In continuation of part - 4, we will see all the important formulas and useful statements which are to be used in the Math test GRE.

Factorization (Continued):

b) Factorization of Polynomial (Continued): 

3) (x - a) (x + b) = x (x + b) - a (x + b)
                          = x ² + b x - a x - ab
                          = x ² - (a - b) x - ab
Generally, we call x ² as the first term, (a + b) x as the middle term, and ab as the last term. 

Basic concept: 

a) Step-1: See the sign of the last term.
b) Step-2: Here it is "-" so factorize the product of the coefficient of the first term (here it is 1) and the last term in such a way that the DIFFERENCE of these two factors must be the coefficient of the middle term.
c) Step-3: Get the factors.

Example-1:

Factorize: x ² - 4 x - 21.

a) Step-1: Here sign of the last term 21 is "-"
b) Step-2: The coefficient of the first term is 1 and the last term is 21, so the product of 1 and 21 is 21. Now the factors of 21 are 3 and 7 and as the sign of the last term is "-", their subtraction is 3 - 7 = -4 which is the coefficient of the middle term. (Note: Here, the coefficient of the middle term is positive so we took it as 3 - 7).  
                         = x ² - 4 x - 21
                         = x ² + (3 - 7) x - (3 x 7)
                         = x ² + 3 x - 7 x - (3 x 7)
                         = x (x + 3) - 7 (x + 3)
                         = (x - 7) (x + 3)
c) Step-3: So the factors of x ² - 4 x - 21 are (x + 3) and (x - 7) 

Example-2:

Factorize: 8 x ² - 18 x - 5.

a) Step-1: Here sign of the last term 5 is "-"
b) Step-2: The coefficient of the first term is 8 and the last term is 5, so the product of 8 and 5 is 8 X 5. Now the factors of 8 X 5 are 2, 2, 2, and 5 and as the sign of the last term is "-", so, we take the two factors in such a way that their difference will be 18. Here 2, 2, 2, and 5 will give us 2 and 20. So, here subtraction is 2 - 20 = -18 which is the coefficient of the middle term.  
                         = 8 x ² - 18 x - 5
                         = 8 x ² + (2 - 20) x - 5
                         = 8 x ² + 2 x - 20 x - 5
                         = 2 x (4 x + 1) - 5 (4 x + 1)
                         = (2 x - 5) (4 x + 1) 
c) Step-3: So the factors of 8 x ² - 18 x + 5 are (2 x - 5) and (4 x + 1).

In the next part, we will see the remaining 1 type in detail. These 1 types are given below.
4) (x - a) (x - b) = x ² - (a + b) x + ab

In the next part, we will see a few examples and some essential formulae.

Click here for the next basics.

ANIL SATPUTE

99-GRE Math-4-Important Key points and formulas

Click here for the previous basics.

In continuation of part - 3, we will see all the important formulas and useful statements which are to be used in the Math test GRE.

Factorization (Continued):

b) Factorization of Polynomial (Continued): 

2) (x + a) (x - b) = x (x - b) + a (x - b)
                          = x ² - b x + a x - ab
                          = x ² + a x - b x - ab
                          = x ² + (a - b) x - ab
Generally, we call x ² as the first term, (a + b) x as the middle term, and ab as the last term. 

Basic concept: 

a) Step-1: See the sign of the last term.
b) Step-2: Here it is "-" so factorize the product of the coefficient of the first term (here it is 1) and the last term in such a way that the DIFFERENCE of these two factors must be the coefficient of the middle term.
c) Step-3: Get the factors.

Example-1:

Factorize: x ² + 4 x - 21.

a) Step-1: Here sign of the last term 21 is "-"
b) Step-2: The coefficient of the first term is 1 and the last term is 21, so the product of 1 and 21 is 21. Now the factors of 21 are 3 and 7 and as the sign of the last term is "-", their subtraction is 7 - 3 = 4 which is the coefficient of the middle term. (Note: Here, the coefficient of the middle term is positive so we took it as 7 - 3).  
                         = x ² + 4 x - 21
                         = x ² + (7 - 3) x - (3 x 7)
                         = x ² + 7 x - 3 x - (3 x 7)
                         = x (x + 7) - 3 (x + 7)
                         = (x - 3) (x + 7)
c) Step-3: So the factors of x ² + 4 x - 21 are (x - 3) and (x + 7) 

Example-2:

Factorize: 8 x ² + 18 x - 5.

a) Step-1: Here sign of the last term 5 is "-"
b) Step-2: The coefficient of the first term is 8 and the last term is 5, so the product of 8 and 5 is 8 X 5. Now the factors of 8 X 5 are 2, 2, 2, and 5 and as the sign of the last term is "-", so, we take the two factors in such a way that their difference will be 18. Here 2, 2, 2, and 5 will give us 2 and 20. So, here subtraction is 20 - 2 = 18 which is the coefficient of the middle term.  
                         = 8 x ² + 18 x - 5
                         = 8 x ² + (20 - 2) x - 5
                         = 8 x ² + 20 x - 2 x - 5
                         = 4 x (2 x + 5) - 1 (2 x + 5)
                         = (2 x + 5) (4 x - 1) 
c) Step-3: So the factors of 8 x ² + 18 x + 5 are (2 x + 5) and (4 x - 1).

In the next part, we will see the remaining 2 types in detail. These 2 types are given below.

3) (x - a) (x + b) = x ² - (a - b) x - ab
4) (x - a) (x - b) = x ² - (a + b) x + ab

In the next part, we will see a few examples and some essential formulae.

Click here for the next basics.

 ANIL SATPUTE

98-GRE Math-3- Important Key points and formulas

Click here for the previous basics.

In continuation of part - 2, we will see all the important formulas and useful statements which are to be used in the Math test GRE.

Factorization (Continued):

b) Factorization of Polynomial: 

Here following 4 possibilities can be studied to understand factorization in a better way.

1) (x + a) (x + b) = x (x + b) + a (x + b)
                          = x ² + b x + a x + ab
                          = x ² + a x + b x + ab
                          = x ² + (a + b) x + ab
2) (x + a) (x - b) = x (x - b) + a (x - b)
                          = x ² - b x + a x - ab
                          = x ² + a x - b x - ab
                          = x ² + (a - b) x - ab
3) (x - a) (x + b) = x (x + b) - a (x + b)
                          = x ² + b x - a x - ab
                          = x ² - a x + b x - ab
                          = x ² - (a - b) x - ab

Note: Here formulae 2 and 3 are of the same type. the coefficient of the middle term is the difference of the Constance and the sign is to be taken from the greater Constance. 
4) (x - a) (x - b) = x (x - b) - a (x - b)
                          = x ² - b x - a x + ab
                          = x ² - a x - b x + ab
                          = x ² - (a + b) x + ab

Now we will study these types in detail:
1) (x + a) (x + b) = x (x + b) + a (x + b)
                          = x ² + b x + a x + ab
                          = x ² + a x + b x + ab
                          = x ² + (a + b) x + ab

Generally, we call x ² as the first term, (a + b) x as the middle term, and ab as the last term. 

Basic concept: 

a) Step-1: See the sign of the last term.
b) Step-2: Here it is "+" so factorize the product of the coefficient of the first term (here it is 1) and the last term in such a way that the SUM of these two factors must be the coefficient of the middle term.
c) Step 3: Get the factors.

Example-1:

Factorize: x ² + 10 x + 21.

a) Step 1: Here sign of the last term 21 is "+"
b) Step 2: The coefficient of the first term is 1 and the last term is 21, so the product of 1 and 21 is 21. Now the factors of 21 are 3 and 7 and as the sign of the last term is "+", their addition is 3 + 7 = 10 which is the coefficient of the middle term.
                         = x ² + 10 x + 21
                         = x ² + (3 + 7) x + (3 x 7)
                         = x ² + 3 x + 7 x + (3 x 7)
                         = x (x + 3) + 7 (x + 3)
                         = (x + 3) (x + 7)
c) Step-3: So the factors of x ² + 10 x + 21 are (x + 3) and (x + 7) 

Example-2:

Factorize: 8 x ² + 14 x + 5.

a) Step 1: Here sign of the last term 5 is "+"
b) Step 2: The coefficient of the first term is 8 and the last term is 5, so the product of 8 and 5 is 8 X 5. Now the factors of 8 X 5 are 2, 2, 2, and 5 and as the sign of the last term is "+", so, we take two factors in such a way that their sum will be 14. Here 2, 2, 2, and 5 will give us 4 and 10. So, here addition is 4 + 10 = 14 which is the coefficient of the middle term.
                         = 8 x ² + 14 x + 5
                         = 8 x ² + (4 + 10) x + 5
                         = 8 x ² + 4 x + 10 x + 5
                         = 4 x (2 x + 1) + 5 (2 x + 1)
                         = (4 x + 5) (2 x + 1)
c) Step 3: So the factors of 8 x ² + 14 x + 5 are (2 x + 1) and (4 x + 5).

In the next part, we will see the remaining 3 types in detail. These 3 types are given below.
2) (x + a) (x - b) = x ² + (a - b) x - ab
3) (x - a) (x + b) = x ² - (a - b) x - ab
4) (x - a) (x - b) = x ² - (a + b) x + ab  

In the next part, we will see a few examples and some essential formulae.

Click here for the next basics.

 ANIL SATPUTE