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(a + b)

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

(a + b)

^{3}= a^{3}+ 3a^{2}b + 3ab^{2}+ b^{3}

(a + b)

^{4}= a^{4}+ 4a^{3}b + 6a^{2}b^{2}+ 4ab^{3}+ b^{4}

a

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

a

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

a

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

a

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

a

^{4}+ b^{4}= (a^{2}+ √2ab + b^{2})(a^{2}- √2ab + b^{2})

a

^{n}- b^{n}= (a - b)(a^{n-1}+ a^{n-2}b + ... + b^{n-1}), for n even

a

^{n}+ b^{n}= (a + b)(a^{n-1}- a^{n-2}b - ... - b^{n-1}), for n odd

Powers and roots:a > 0, b > 0, x, y real

a

^{x}a^{y}= a^{x+y}

a

^{x}/ a^{y}= a^{x-y}

a

^{x}b^{x}= (ab)^{x}

a

^{x}/ b^{x}= (a / b)^{x}

a

^{-x}= 1 / a^{x}

If a / b = c / d, then (a ± b) / b = (c ± d) / d, and (a - b) / (a + b) = (c - d) / (c + d)

Common Irrational Numbers (includes the first 12 prime numbers):

To find the root of a number which is not prime – do a prime factorization of the number and multiply / exponentiate appropriately.

For example,

College Algebra (Schaum's Outlines)

The classic algebra problem book - very light on theory, plenty of problems with full solutions, more problems with answers

Schaum's Easy Outline: College Algebra

A simplified and updated version of the classic Schaum's Outline. Not as complete as the previous book, but enough for most students