Monomials

axn + bxn = (a + b)xn

axn · bxm = (a · b)xn + m

axn : bxm = (a : b)xn − m

(axn)m = am · xn · 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

Mm x n x Mn 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
a32.

Rule of Sarrus

+ sign

− sign

Cramer's Rule

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.

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