Maths equations

Some Important Maths Equations 

1. a(b+c) = ab + ac
2. (a+b)² = a² + 2ab + b²

3. (a-b)² = a²-2ab + b²

4. (a+b)² = (a-b)² + 4ab

5. (a-b)² = (a+b)² - 4ab 
6. (a-b) (a+b) = a² - b²

7. (a+b)³ = a³ + 3ab(a+b) + b³
8. (a-b)³ = a³ - 3ab(a-b) - b³
9. a³ + b ³ = (a+b) (a² - ab + b²)
10. a³ - b ³ = (a-b) (a² + ab + b²)
11. (a³ - b³) / (a² + ab + b²) = a-b
12. (a³ + b³) / (a² - ab + b²) = a+b
__________________________________________________________________________________ 
How to use these equations in exams.

1. (4.75 x 4.75 x 4.75 + 1.25 x 1.25 x 1.25) / ( 4.75 x 4.75 + 1.25 x 1.25 - 4.75 x 1.25) = ?
If you saw a question like this, you can use these equations to find its answer. If try to solve these question without using equation you gonna take too much time , thats what the examiners want. 

= (4.75³ + 1.25³) / (4.75² + 1.25³ - 4.75 x 1.25)

now it is same like in the 12^th equation (a³ + b³) / (a² - ab + b²) = a+b

ie. = 4.75 + 1.25
 = 6