College Algebra

# Key Equations

College AlgebraKey Equations
 Rules of Exponents For nonzero real numbers$a a$and$b b$and integers$m m$and$n n$ Product rule $a m ⋅ a n = a m+n a m ⋅ a n = a m+n$ Quotient rule $a m a n = a m−n a m a n = a m−n$ Power rule $( a m ) n = a m⋅n ( a m ) n = a m⋅n$ Zero exponent rule $a 0 =1 a 0 =1$ Negative rule $a −n = 1 a n a −n = 1 a n$ Power of a product rule $( a⋅b ) n = a n ⋅ b n ( a⋅b ) n = a n ⋅ b n$ Power of a quotient rule $( a b ) n = a n b n ( a b ) n = a n b n$
 perfect square trinomial $(x+a) 2 =(x+a)(x+a)= x 2 +2ax+ a 2 (x+a) 2 =(x+a)(x+a)= x 2 +2ax+ a 2$ difference of squares $(a+b)(a−b)= a 2 − b 2 (a+b)(a−b)= a 2 − b 2$
 difference of squares $a 2 − b 2 =(a+b)(a−b) a 2 − b 2 =(a+b)(a−b)$ perfect square trinomial $a 2 +2ab+ b 2 = (a+b) 2 a 2 +2ab+ b 2 = (a+b) 2$ sum of cubes $a 3 + b 3 =(a+b)( a 2 −ab+ b 2 ) a 3 + b 3 =(a+b)( a 2 −ab+ b 2 )$ difference of cubes $a 3 − b 3 =(a−b)( a 2 +ab+ b 2 ) a 3 − b 3 =(a−b)( a 2 +ab+ b 2 )$