Monomials

axⁿ + bxⁿ = (a + b)xⁿ

axⁿ · bx^m = (a · b)x^{n + m}

axⁿ : bx^m = (a : b)x^{n − m}

(axⁿ)^m = a^m · x^{n · m}

Binomials

(a ± b)² = a² ± 2 · a · b + b²

(a + b) · (a − b) = a² − b²

(a ± b)³ = a³ ± 3 · a² · b + 3 · a · b² ± b³

a³ + b³ = (a + b) · (a² − ab + b²)

a³ − b³ = (a − b) · (a² + ab + b²)

(x + a) (x + b) = x² + (a + b) x + ab

Binomial Formula

Trinomials

(a + b + c)² = a² + b² + c² + 2 · a · b + + 2 · a · c + 2 · b · c

a x² + bx +c = 0 a · (x -x₁ ) · (x -x₂ ) = 0

Quadratic Formula

ax² + bx + c = 0,    a ≠ 0.

ax² = 0

x = 0

ax² + bx = 0

x (ax + b) = 0

x = 0

ax² + c = 0

S = x₁ + x₂

P = x₁ · x₂

a x² + bx +c = 0

a · (x -x₁ ) · (x -x₂ ) = 0

ax⁴ + bx² + c = 0

Matrix Formulas

M_{m x n} x M_{n x p} = M _{m x p}

Matrix Inverse

A · A^-1  = A^-1 · A = I

(A · B)^-1  = B^-1 · A^-1

(A^-1)^-1  = A

(k · A)^-1  = k^-1 · A^-1

Determinants Formulas

Determinant of Order One

  |a₁₁| = a₁₁

Determinant of Order Two

   = a ₁₁ a ₂₂ - a ₁₂ a ₂₁

Determinant of Order Three

=

a₁₁ a₂₂ a₃₃ + a₁₂ a₂₃ a ₃₁ + a₁₃ a₂₁ a₃₂ -

- a ₁₃ a₂₂ a₃₁ - a₁₂ a₂₁ a ₃₃ - a₁₁ a₂₃ a_32.

Rule of Sarrus

+ sign

− sign

Cramer's Rule

•  
• 
•