Algebra Formula

Algebra is a branch of Mathematics that substitutes letters for numbers. The numbers are constants. Algebra also includes real numbers, complex numbers, matrices, vectors and much more. X, Y, A, B are the most commonly used letters that represent the algebraic problems and equation 1/b.

Important Formulas in Algebra

Real Numbers : a, b, c, x, y, z
Natural Number : n, m

Factoring 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)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)
(x + y + z)²= x²+ y²+ z²+ 2xy + 2yz + 2xz
(x + y − z)²= x² + y² + z² + 2xy − 2yz − 2xz
(x − y + z)²= x² + y² + z² − 2xy − 2yz + 2xz
(x − y − z)²= x² + y² + z² − 2xy + 2yz − 2xz
x³ + y³ + z³ −3xyz = (x + y + z)(x² + y²+ z²− xy − yz − xz)
x² + y²= 1/2 [(x + y)²+ (x − y)²]
(x + a)(x + b)(x + c) = x³+ (a + b + c)x²+ (ab + bc + ca)x + abc
x³ + y³ = (x + y)(x² − xy + y²)
x³ − y³ = (x − y)(x² + xy + y²)
x² + y²+ z²− xy − yz − zx = 1/2[(x − y)² + (y − z)² + (z − x)²]
If n is a natural number, aⁿ − bⁿ = (a − b)(aⁿ⁻¹ + aⁿ⁻²b + … + 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 + bc + ….)
Laws of Exponents
- (a^m)(aⁿ) = a^m+n
- (ab)^m = a^mb^m
- (a^m)ⁿ = a^mn
Fractional Exponents
- a⁰ = 1
- a^m/aⁿ = a^m−n
- a^m = 1/a^−m
- a^−m = 1/a^m