Short multiplication formulas

Square of sum:

(a + b)² = a² + 2ab + b²

Square of difference:

(a − b)² = a² − 2ab + b²

Cube of sum:

(a + b)³ = a³ + 3a²b + 3b²a + b³

Cube of difference:

(a − b)³ = a³ − 3a²b + 3b²a − b³

Binomal theorem:

(a + b)ⁿ = C₀ⁿaⁿ + C₁ⁿaⁿ⁻¹b + ... + C_kⁿa^n−kb^k + C_nⁿbⁿ , coefficients C_kⁿ = n! / [k!(n − k)!]

Sum of squares:

a² + b² - not expands

Difference of squares:

a² − b² = (a − b)(a + b)

Sum of cubes:

a³ + b³ = (a + b)(a² − ab + b²)

Difference of cubes:

a³ − b³ = (a − b)(a² + ab + b²)