Short multiplication formulas

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Square of sum:

(a + b)2 = a2 + 2ab + b2

Square of difference:

(ab)2 = a2 2ab + b2

Cube of sum:

(a + b)3 = a3 + 3a2b + 3b2a + b3

Cube of difference:

(ab)3 = a3 3a2b + 3b2a b3

Binomal theorem:

(a + b)n = C0nan + C1nan1b + ... + Cknankbk + Cnnbn , coefficients Ckn = n! / [k!(n − k)!]

Sum of squares:

a2 + b2 - not expands

Difference of squares:

a2b2 = (ab)(a + b)

Sum of cubes:

a3 + b3 = (a + b)(a2ab + b2)

Difference of cubes:

a3b3 = (ab)(a2 + ab + b2)