Here is a list of important algebraic formulas that you would probably find very helpful during your preparations and also to refresh your basics.

- Square Formulas -

(a+b)² = a²+ 2ab + b²

(a – b)² = a² – 2ab + b²

a² – b² = (a – b)(a + b)

(x+a)(x+b) = x² +(a+b)x + ab

(a + b + c)² = a²+ b² + c² + 2ab + 2ac + 2bc

(a – b – c)² = a² + b² + c²– 2ab – 2ac + 2bc

((a+(-b)+(-c))² = a² + (-b)² + (-c)² +2a(-b)+2(-b)(-c)+ 2a(-c)

- Cube Formulas -

(a + b)3 = a3 + 3a2b + 3ab2 + b3

(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 + b3 + 3ab(a + b)

   a3 + b3 + c3 – 3abc = (a+b+c) (a2+b2+c2 – ab – bc – ac)

- Power n Formula -

an – bn = (a – b)(an-1 + an-2b+…+ bn-2a + bn-1)

- Laws of Exponents -

√a = a¼

a0 = 1

3√a =  a1/3

n√a =  a1/n

(am)(an) = am+n

am/ an = am-n

 (ab)m = ambm

(am)n = amn

- Irrational Numbers -

√ab = √a √b

(√a  + √b)  - (√a  - √b) = a - b

(√a  + √b)² = a + 2√ab + b

(a  + √b)(a  - √b) = a² - b

- Roots of Quadratic Equation -

 

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