1. (a + b)(a – b) = a2 – b
2. (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
3. (a ± b)2 = a2 + b2± 2ab
4. (a + b + c + d)2 = a2 + b2 + c2 + d2 + 2(ab + ac + ad + bc + bd + cd) 5. (a ± b)3 = a3 ± b3 ± 3ab(a ± b)
6. (a ± b)(a2 + b2 m ab) = a3 ± b3
7. (a + b + c)(a2 + b2 + c2 -ab – bc – ca) = a3 + b3 + c3 – 3abc = 1/2 (a + b + c)[(a - b)2 + (b - c)2 + (c - a)2] 8. when a + b + c = 0, a3 + b3 + c3 = 3abc
9. (x + a)(x + b) (x + c) = x3 + (a + b + c) x2 + (ab + bc + ac)x + abc 10. (x – a)(x – b) (x – c) = x3 – (a + b + c) x2 + (ab + bc + ac)x – abc 11. a4 + a2b2 + b4 = (a2 + ab + b2)( a2 – ab + b2)

12. a4 + b4 = (a2 – √2ab + b2)( a2 + √2ab + b2)
13. an + bn = (a + b) (a n-1 – a n-2 b + a n-3 b2 – a n-4 b3 +…….. + b n-1) (valid only if n is odd)
14. an – bn = (a – b) (a n-1 + a n-2 b + a n-3 b2 + a n-4 b3 +……… + b n-1) {where n ϵ N)
15. (a ± b)2n is always positive while -(a ± b)2n is always negative, for any real values of a and b 16. (a – b)2n = (b – a)2” and (a – b)2n+1 = – (b – a)2n+1 17. if α and β are the roots of equation ax2 + bx + c = 0, roots of cx” + bx + a = 0 are 1/α and 1/β. if α and β are the roots of equation ax2 + bx + c = 0, roots of ax2 – bx + c = 0 are -α and -β. 18.

* n(n + l)(2n + 1) is always divisible by 6.
* 32n leaves remainder = 1 when divided by 8
* n3 + (n + 1 )3 + (n + 2 )3 is always divisible by 9
* 102n + 1 + 1 is always divisible by 11
* n(n2- 1) is always divisible by 6
* n2+ n is always even
* 23n-1 is always divisible by 7
* 152n-1 +l is always divisible by 16
* n3 + 2n is always divisible by 3
* 34n – 4 3n is always divisible by 17
* n! + 1 is not divisible by any number between 2 and n (where n! = n (n – l)(n – 2)(n – 3)…….3.2.1)
for eg 5! = 5.4.3.2.1 = 120 and similarly 10! = 10.9.8…….2.1= 3628800 19. Product of n consecutive numbers is always divisible by...

...The Euler’s Formula
Euler’s formula and Identity: eix = cos(x) + i(sin(x))
The world of math today is one with endless possibilities. It expands into many different and interesting topics, often being incorporated into our everyday lives. Today, I will talk about one of these topics; the most mind-blowing and fascinating formula invented, called the “Euler’s formula”. This formula was created and...

...Opposite
Cot = 1/tan
Sec= 1/sin
Csc = 1cos
Special rules
| 300 | 450 | 600 |
Sin | 12 | 12 | 32 |
Cos | 32 | 12 | 12 |
tan | 13 | 1 | 2
2
3
300
600
1
1
3 |
2
450
1
1
Area of triangle
There is an basic formula for finding the area of a triangle A=12BH but I’m going to look at how to find the area of a triangle WITHOUT the base OR the height.
X
Y
Z
As long were are given x,y AND z we can find the area of this triangle without...

...- Politeness formulas in Arabic:
When talking about politeness formulas in Arabic and in English and how they are different, it is crucial to take into account the distinction between propositional content of a formula and its illocutionary force potential. A good example showing the relationship between semantic content or propositional content and illocutionary force illustrates in using congratulations in English and “shukran” in Arabic...

...benefits of different types of formula that are commonly available
Breast milk is a natural form of baby food which is perfect for a baby. But there are some people who for different reasons can’t breastfeed, or have chosen not to, formula milk is the next best thing.
Scientists and medical experts have spent years developing high-quality formula milks that will provide babies with the specific nutrition that they need.
There are many...

...Marketing Research Project
Pricing strategy for ‘Formula One India Racing Event’ for Retail Customers
Table of Contents
1. Marketing Research Objective: 3
2. Introduction 3
3. Mode of survey 5
4. Survey Questionnaire 6
5. References 8
1. Marketing Research Objective
What should be optimal price for different classes of tickets at ‘Formula One India Racing Event’ for Retail Customers?
1. Introduction
Formula One is the...

...
In Mathematics, a periodic function is a function that repeats its values in regular intervals or periods. Periodic functions are used throughout science to describe oscillations, waves, and other phenomena that exhibit periodicity.
Periodic functions are those that repeat on a set interval. All trigonometric functions are periodic. They are useful because one can determine the value of the function anywhere in the domain. If a function is periodic, then there is some value n for...

...Innovating new packaging by determining the best suitable level of efficiency with the use of calculus for Trini Chocolate Delights.
JABARI BOWMAN
ADD MATH
SBA
CLASS: 5-6
SCHOOL: ST. MARY’S COLLEGE
TEACHER: MR. YIP-YOUNG
Problem Statement
The project’s purpose is to work out the best level of production to suit the new packaging for ‘Trini Chocolate Delights ltd.’
The company’s objective is to maximize produce of their new product but minimize manufacturing cost. To...