Mathematical formulas

Algebra

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1Numbers and algebraic properties
2Powers, exponents, and radicals
3Algebraic expressions
4Notable products and identities
5Factorization
6Rational expressions and partial fractions
7Equations
8Inequalities
9Systems of equations
10Functions
11Polynomials
12Exponentials and logarithms
13Complex numbers
14Sequences, finite series, and recurrences
15Vectors
16Matrices
17Determinants and inverses
18Vector spaces
19Linear transformations
20Eigenvalues and diagonalization
21Orthogonality and projections
22Least squares
23Matrix decompositions
24Matrix norms and conditioning
25Boolean algebra
26Modular arithmetic
27Algebraic structures
28Linear codes and error correction
29Relationship maps

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Subjects
Algebra
Notable products and identities

Section 4

Notable products and identities

Square of a sum

fundamentalviz

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

Expansion of the square of a binomial.

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Square of a difference

fundamentalviz

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

Expansion of the square of a difference.

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Difference of squares

fundamentalviz

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

Identity for expansion and factorization.

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fundamental

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

Expansion of the cube of a binomial.

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Cube of a difference

fundamental

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

Expansion of the cube of a difference.

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fundamental

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

Factorization of a sum of cubes.

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Difference of cubes

fundamental

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

Factorization of a difference of cubes.

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Binomial theorem

intermediateviz

(a + b)^{n} = k = 0 \sum n (k n) a^{n - k} b^{k}

Generalizes powers of binomials.

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