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Algebra Formulae

Algebra

Factors and expansions a, b real; n positive integer

(a b) = a 2ab + b

(a b) = a 3ab + 3ab b

(a b)4 = a4 4ab + 6ab 4ab + b4

a - b = (a - b)(a + b)

a + b = (a - bi)(a + bi)

a - b = (a - b)(a + ab + b)

a + b = (a + b)(a - ab + b)

a4 + b4 = (a + 2ab + b)(a - 2ab + b)

an - bn = (a - b)(an-1 + an-2b + ... + bn-1), for n even

an + bn = (a + b)(an-1 - an-2b - ... - bn-1), for n odd

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

axay = ax+y

ax / ay = ax-y

axbx = (ab)x

ax / bx = (a / b)x

a-x = 1 / ax

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Proportion

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

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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,

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Recommended Algebra Books

cover College Algebra (Schaum's Outlines)

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

 

cover 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

 

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