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Important and Useful Rules/Formulas

Module by: Denny Burzynski, Wade Ellis. E-mail the authors

Summary: This module contains a chart of important and useful rules/formulas from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr.

Exponents (Assume each expression is defined.)

a n a m = a n + m a n a m = a n + m

a n a m = a n - m a n a m = a n - m

( a n ) m = a nm ( a n ) m = a nm

( ab ) n = a n b n ( ab ) n = a n b n

a - 1 = 1 a a - 1 = 1 a

a - n = 1 a n a - n = 1 a n

a 0 = 1 a 0 =1

( a b ) n = a n b n ( a b ) n = a n b n

Factorization and special product formulas

ab + ac = a ( b + c ) ab+ac=a(b+c)

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

a 2 - b 2 = ( a + b ) ( a - b ) a 2 - b 2 =(a+b)(a-b)

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

Formulas

x = - b ± b 2 - 4 a c 2 a Quadratic formula y = m x + b Slope-intercept form of a straight line y - y 1 = m ( x - x 1 ) Point-slope form of a straight line m = y 2 - y 1 x 2 - x 1 Slope of a straight line passing through the points ( x 1 , x 2 ) and ( y 1 , y 2 ) x = - b ± b 2 - 4 a c 2 a Quadratic formula y = m x + b Slope-intercept form of a straight line y - y 1 = m ( x - x 1 ) Point-slope form of a straight line m = y 2 - y 1 x 2 - x 1 Slope of a straight line passing through the points ( x 1 , x 2 ) and ( y 1 , y 2 )

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