All Algebraic Formulas in Maths

Algebra is a branch of mathematics that deals with the study of mathematical symbols and the rules for manipulating these symbols. It is an essential subject for students who wish to pursue careers in science, engineering, economics, and many other fields. Algebraic formulas are an integral part of algebra and are used to solve equations and simplify expressions. In this article, we will discuss all the important algebraic formulas that every student should know.

Basic Formulas:

(a + b)^2 = a^2 + 2ab + b^2

(a - b)^2 = a^2 - 2ab + b^2

(a + b)(a - b) = a^2 - b^2

(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3

(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ac

Quadratic Formulas:

The quadratic formula is used to solve quadratic equations of the form ax^2 + bx + c = 0.

x = (-b ± sqrt(b^2 - 4ac))/2a

Exponential and Logarithmic Formulas:

a^m * a^n = a^(m+n)

a^m/a^n = a^(m-n)

(a^m)^n = a^(mn)

a^0 = 1

a^-n = 1/a^n

log a (xy) = log a (x) + log a (y)

log a (x/y) = log a (x) - log a (y)

log a (x^n) = n log a (x)

Trigonometric Formulas:

sin^2(x) + cos^2(x) = 1

1 + tan^2(x) = sec^2(x)

1 + cot^2(x) = csc^2(x)

sin(a ± b) = sin(a)cos(b) ± cos(a)sin(b)

cos(a ± b) = cos(a)cos(b) ∓ sin(a)sin(b)

tan(a ± b) = (tan(a) ± tan(b))/(1 ∓ tan(a)tan(b))

Factorization Formulas:

a^2 - b^2 = (a + b)(a - b)

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

a^2 + 2ab + b^2 = (a + b)^2

a^2 - 2ab + b^2 = (a - b)^2

Complex Number Formulas:

(i^0 = 1, i^1 = i, i^2 = -1, i^3 = -i)

(i^4n = 1, i^(4n+1) = i, i^(4n+2) = -1, i^(4n+3) = -i)

(a + bi) + (c + di) = (a + c) + (b + d)i

(a + bi) - (c + di) = (a - c) + (b - d)i

(a + bi)(c + di) = (ac - bd) + (ad + bc)i