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# Factoring: Some special cases

Here are some algebraic formulas, which can be used for factoring and simplifications of expressions. All of them can be proved disclosing of brackets and collecting like terms of items.

## The binomials formulas

 (a + b)2 = a2 + 2ab + b2 – square of the sum (a – b)2 = a2 – 2ab + b2 – square of the difference a2 – b2 = (a – b)(a + b) – difference of squares (a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc

## The trinomials formulas

 (a + b)3 = a3 + 3a2b + 3ab2 + b3 – cubes of the sum (a – b)3 = a3 – 3a2b + 3ab2 – b3 – cubes of the difference a3 + b3 = (a + b)(a2 – ab + b2) – sum of cubes a3 – b3 = (a – b)(a2 + ab + b2) – difference of cubes

## The formulas for the fourth degree

 (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4 (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4 a4 – b4 = (a – b)(a + b)(a2 + b2)

## Binomial theorem

 (a + b)n = an + nan – 1b + n(n – 1)2an – 2b2 + ... + n!k!(n – k)!an – kbk + ... + bn (a - b)n = an - nan – 1b + n(n – 1)2an – 2b2 + ... + (-1)kn!k!(n – k)!an – kbk + ... + (-1)nbn