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(a ± b)² = a² ± 2ab + b²

(a ± b)³ = a³ ± 3a²b + 3ab² ± b³

(a ± b)

^{4}= a^{4}± 4a³b + 6a²b² ± 4ab³ + b^{4}

a² - b² = (a - b)(a + b)

a² + b² = (a - bi)(a + bi)

a³ - b³ = (a - b)(a² + ab + b²)

a³ + b³ = (a + b)(a² - ab + b²)

a

^{4}+ b^{4}= (a² + 2^{½}ab + b²)(a² - 2^{½}ab + b²)

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 rootsa > 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