Algebra Formulas

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

Binomial Formula

Binomial Coefficient

Properties of the Binomial Coefficient

Properties of the Binomial Coefficient


Pascal´s Triangle


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.

Quadratic Formula


ax2 = 0

x = 0

ax2 + bx = 0

x (ax + b) = 0

x = 0

Quadratic Solution

ax2 + c = 0

Quadratic Solution


Quadratic Solution

Quadratic Solution


Quadratic Expression

S = x1 + x2

P = x1 · x2

a x2 + bx +c = 0

a · (x -x1 ) · (x -x2 ) = 0


ax4 + bx2 + c = 0

Quadratic Solution


Matrix Formulas

Matrix Addition

Matrix Subtraction

Real Number and Matrix Product


Mm x n x Mn x p = M m x p

Real Number and Matrix Product


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

Inverse Matrix

Matrix Inverse

Matrix Determinant

Adjugate Matrix

Transpose of the Adjugate Matrix


Determinants Formulas

Determinant of Order One

  |a11| = a11

Determinant of Order Two

  Determinant of Order Two = a 11 a 22 - a 12 a 21


Determinant of Order Three

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

Rule of Sarrus-Positive+ sign

Rule of Sarrus-Negative− sign


Cramer's Rule

Cramer's Rule

Cramer's Rule

Cramer's Rule

Cramer's Rule

Cramer's Rule

Cramer's Rule

Cramer's Rule