Basic maths formulas (Part-1)

list of Algebraic formulas :

• a2 – b2 = (a – b)(a + b)
• (a+b)2 = a2 + 2ab + b2
• a2 + b2 = (a – b)2 + 2ab
• (a – b)2 = a2 – 2ab + b2
• (a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc
• (a – b – c)2 = a2 + b2 + c2 – 2ab – 2ac + 2bc
• (a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
• (a – b)3 = a3 – 3a2b + 3ab2 – b3
• a3 – b3 = (a – b)(a2 + ab + b2)
• a3 + b3 = (a + b)(a2 – ab + b2)
• (a + b)3 = a3 + 3a2b + 3ab2 + b3
• (a – b)3 = a3 – 3a2b + 3ab2 – b3
• (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4)
• (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4)
• a4 – b4 = (a – b)(a + b)(a2 + b2)
• a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)
• If n is a natural number, an – bn = (a – b)(an-1 + an-2 +…+ bn-2a + bn-1)
• If n is even (n = 2k), an + bn = (a + b)(an-1 – an-2b +…+ bn-2a – bn-1)
• If n is odd (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b +…- bn-2a + bn-1)
• (a + b + c + …)2 = a2 + b2 + c2 + … + 2(ab + ac + bc + ….
• Laws of Exponents(am)(an) = am+n(ab)m = ambm(am)n = amn

Fractional Exponents
a0 = 1
aman=am−n
am$a^m$ = 1a−m




Average formula: 

Let a₁,a₂,a₃,......,a_n be a set of numbers, avera
ge = (a₁ + a₂ + a₃,+......+ a_n)/n

Fractions formulas: 

Converting an improper fraction to a mixed number:

Formula for a proportion: 

In a proportion, the product of the extremes (ad) equal the product of the means(bc), 

Thus, ad = bc

Percent: 

Percent to fraction: x% = x/100

Percentage formula: Rate/100 = Percentage/base

Rate: The percent. 
Base: The amount you are taking the percent of.
Percentage: The answer obtained by multiplying the base by the rate

Consumer math formulas: 

Discount = list price × discount rate

Sale price = list price − discount

Discount rate = discount ÷ list price

Sales tax = price of item × tax rate

Interest = principal × rate of interest × time

Tips = cost of meals × tip rate

Commission = cost of service × commission rate

Geometry formulas: 

Perimeter:

Perimeter of a square: s + s + s + s 
s:length of one side

Perimeter of a rectangle: l + w + l + w
l: length
w: width

Perimeter of a triangle: a + b + c
a, b, and c: lengths of the 3 sides

Area:

Area of a square: s × s 
s: length of one side

Area of a rectangle: l × w
l: length
w: width

Area of a triangle: (b × h)/2
b: length of base
h: length of height

Area of a trapezoid: (b₁ + b₂) × h/2
b₁ and b₂: parallel sides or the bases
h: length of height

volume:

Volume of a cube: s × s × s 
s: length of one side

Volume of a box: l × w × h
l: length
w: width
h: height

Volume of a sphere: (4/3) × pi × r³
pi: 3.14
r: radius of sphere

Volume of a triangular prism: area of triangle × Height = (1/2 base × height) × Height
base: length of the base of the triangle
height: height of the triangle
Height: height of the triangular prism

Volume of a cylinder:pi × r² × Height
pi: 3.14
r: radius of the circle of the base
Height: height of the cylinder