# All Basic-algebra Formulas List

## GP (Geometric Progression)

#### Formula:

Gp = [a r (n-1)]

Where,

a - first term in the series,
n - last term in the series,
r - common difference.

## Team Work

#### Formula:

Group work = 1 / ((1 / a) + (1 / b))

Where,
a - Workdone by a in days or hours
b - Workdone by b in days or hours

## Sum of Consecutive Squares

#### Formula:

Sum of consecutive squares = ( ( n * ( n + 1 ) * ( 2n + 1 ) ) / 6)

## Multiply Binomial

#### Example :

Multiplying two Binomials using FOIL method,
(3x - 4) and (2x +1)
Using FOIL Method,
Multiply the First Terms :
(3x) × (2x) = 6x2
Multiply the Outside Terms :
(3x) × (1) = 3x
Multiply the Inside Terms :
(-4) × (2x) = - 8x
Multiply the Last Terms :
(-4) × (1) = - 4
Binomial Equation = ( 6x2 + 3x - 8x - 4 ) = 6x2 - 5x - 4.

## Complex Number

#### Complex Number Formula:

Multiplication = (a+bi) × (a+bi)
Division = (a+bi) / (a+bi)
Square root:
r = sqrt(a² + b²)
y = sqrt((r-a) / 2)
x = b / 2y
r1 = x + yi
r2 = -x - yi

## Arithmetic Progression (AP)

#### Formula:

Arithmetic Progression = a + (n-1)* d

Where,

a - the first term in the series,
n - last term in the series and
d - Common difference.

## Sum of Consecutive Cubes

#### Formula:

The Sum of consecutive cubes are calculated using the formula

Sum of consecutive cubes = ( ( n 2 × (n+1) 2 ) / 4 )

Where,

Nth term

## Sum of Two Cubes

#### Formula Used to calculate the sum of two cube:

Perfect Cubes Addition = a3 + b3

Let us consider 2 numbers say a and b
Cube of the first number = a3
Cube of the second number = b3
Sum of two cubes = cube of the first number + cube of the second number.

## Fibonacci Series

#### Formula:

F(0)=0; F(1)=1; F(n) = F(n-1) + F(n-2), n>1

## Stirlings Factorial

#### Stirling's Factorial Formula:

n! ≈   √(2π) × n(n+1/2) × e -n

Where,

n = Number of elements

## Mod

#### Formula:

Modulo Remainder of Division Value (a % b)

Where,

a is first numeric value
b is second numeric value

## Complex Conjugate

#### Formula:

z = a + bi = a - bi

Where,

a - Real Part of z
b - Imaginary Part of z

## Sum of Squares

#### Formula:

S = a2 + b2 + c2 + d2

Where,

a,b,c,d are integers
S is the Sum of Squares of the integers a,b,c,d

## Angle Between Two Lines

Formula: Where,

u1, u2, u3 = coordinates of U vector
v1, v2, v3 = coordinates of V vector

## Complex Number to Polar

Formula:

z = r ( cos ϑ + i sin ϑ )
r = √x2 + y2ϑ = tan-1 (y / x)

Where,

x, y - triangle sides
r - Modulus of complex number
z - Polar representation
ϑ - Angle

## Modulus of Complex Number

#### Formula:

|z| = |a + bi| = √a2 + b2

where

a,b - real number,
i - imaginary number

## Floyds Triangle

Formula:
Sum Row(n)=n(n2+1)/2

Where

n - nth Row of Triangular Array of Numbers

## Triangle Angle Bisector

#### Formula:

L = √((a*b)*(a+b+c)(a+b-c)) / (a+b)

Where,

L = Length of Angle Bisector
a = Side1
b = Side2
c = Side3

## Vertex

#### Formula:

h = -b / 2a
k = c - (b2 / 4a)

Where,

h,k = Vertex of the Quadratic Equation
a,b,c = Points

## Eccentricity Of An Ellipse

#### Formula

E = (√a2-b2) / a

where,
E = Eccentricy of an Ellipse,
a = Ellipse major axis,
b= Ellipse minor axis

## Proportion

#### Formula:

A / B= C / ?

Where,

A,B,C are known values
?=B x C / A

## Angle Bisector of a Triangle

#### Formula Used:

|A1X+B1Y+C1|/√A12+B12=±|A2X+B2Y+C2|/√A22+B22

Where,

A1,B1,C1,A2,B2,C2 = Coefficients
X,Y = Coordinates

## Leibniz Harmonic Triangle

#### Formula:

an,k = 1 / k (nCk)

Where

n - no of rows
k - no of columns for each row
C - binomial coefficient

## Simpson 3/8 Rule for Integration

#### Formula: Where

xk = a + kh
k = 0,1,...3m

## Tangent line of Parabola

#### Formula

m=dy/dx
tangent line => y-y0=m(x-x0)

## Solution of Cubic Root

#### Formula:

xn = yn - (b / 3a)

Where,

xn, yn = Cubic Root
a, b = Real Constant

## Distance Perspective Projection

#### Formula:

L = D / (2 * tan(α/2))

Where,

L = Distance to the Object
D = Linear Size
α = Angular Size

## Angular Size

#### Formula:

α=2*arctan(d/(2*L))

Where,

α = Angular Diameter
d = Linear Size
L = Distance to Object

## Linear Size

#### Formula:

D =2* L * (Tan*(α/2))

Where,

D =Linear Size
L = Distance to the Object
α = Angular Size

## Relative Percentage Difference

#### Formula :

Relative Percentage Difference = (|Num1-Num2|/((Num1+Num2)/2)) x 100

Where,

Num1= Original Number
Num2= Second Number

## Fourth Root

#### Formula:

b = 4√ (a)

Where,

b = Fourth Root Value
a = Input Value

## Difference of Cubes Calculator

#### Formula:

C = (A3 - B3) = (A - B) * (A2 + A*B + B2)

Where,

C = Difference of Two Cubes
A, B = Input Values

## Difference Quotient

#### Formula :

Difference quotient = (f(x+h)-f(x))/h

## Angle Between Two Vectors

#### Formula:

r = arccos ( ( a * x ) + ( b * y ) + ( c * z ) ) / ( √( a2 + b2 + c2) * √( x2 + y2 + z2) )

Where,

r = Angle Between Two vectors
a = i1 Co-efficient
b = j1 Co-efficient
c = k1 Co-efficient
x = i2 Co-efficient
y = j2 Co-efficient
z = k2 Co-efficient

## Difference Between Two Cube

#### Formula:

(a3 - b3)=(a - b)(a2 + ab + b2)

Where,

a = First cube value
b = Second cube value

## Sum and Difference of Cubes

#### Sum of Cubes Formula:

a3 + b3 = ( a + b ) (a2 - ab + b2)

#### Difference of Cubes Formula:

a3 - b3 = ( a - b ) (a2 + ab + b2)

Where,

a, b are values