Basic Algebra Cheat Sheet, Cheat Sheet of Algebra

Download Basic Algebra Cheat Sheet and more Cheat Sheet Algebra in PDF only on Docsity! Algebra Cheat Sheet Basic Properties & Facts Arithmetic Operations ( ) , 0 b abab ac a b c a c c a a a acb bc bc b c a c ad bc a c ad bc b d bd b d bd a b b a a b a b c d d c c c c a ab ac adbb c a ca bc d  + = + =          = =       + − + = − = − − + = = + − −    +  = + ≠ =       Exponent Properties ( ) ( ) ( ) ( ) 11 0 1 1, 0 1 1 n mm m n n m n m n m m m n mn nm n n n n n n n n n n n n n n n n aa a a a a a a a a a a aab a b b b a a a a a b b a a a b a a + − − − − − = = = = = ≠  = =    = =    = = = =        Properties of Radicals 1 , if is odd , if is even nn n n n n m n nm n n n n n n a a ab a b a aa a b b a a n a a n = = = = = = Properties of Inequalities If then and If and 0 then and If and 0 then and a b a c b c a c b c a ba b c ac bc c c a ba b c ac bc c c < + < + − < − < > < < < < > > Properties of Absolute Value if 0 if 0 a a a a a ≥ = − < 0 Triangle Inequality a a a aaab a b b b a b a b ≥ − = = = + ≤ + Distance Formula If ( )1 1 1,P x y= and ( )2 2 2,P x y= are two points the distance between them is ( ) ( ) ( )2 21 2 2 1 2 1,d P P x x y y= − + − Complex Numbers ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) 2 2 2 2 2 2 1 1 , 0 Complex Modulus Complex Conjugate i i a i a a a bi c di a c b d i a bi c di a c b d i a bi c di ac bd ad bc i a bi a bi a b a bi a b a bi a bi a bi a bi a bi = − = − − = ≥ + + + = + + + + − + = − + − + + = − + + + − = + + = + + = − + + = + Logarithms and Log Properties Definition log is equivalent to yby x x b= = Example 3 5log 125 3 because 5 125= = Special Logarithms 10 ln log natural log log log common log ex x x x = = where 2.718281828e = … Logarithm Properties ( ) ( ) log log 1 log 1 0 log log log log log log log log log b b b xx b r b b b b b b b b b b x b x x r x xy x y x x y y = = = = = = +   = −    The domain of logb x is 0x > Factoring and Solving Factoring Formulas ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 22 2 22 2 2 2 2 x a x a x a x ax a x a x ax a x a x a b x ab x a x b − = + − + + = + − + = − + + + = + + ( ) ( ) ( )( ) ( ) ( ) 33 2 2 3 33 2 2 3 3 3 2 2 3 3 2 2 3 3 3 3 x ax a x a x a x ax a x a x a x a x a x ax a x a x a x ax a + + + = + − + − = − + = + − + − = − + + ( )( )2 2n n n n n nx a x a x a− = − + If n is odd then, ( ) ( ) ( )( ) 1 2 1 1 2 2 3 1 n n n n n n n n n n n x a x a x ax a x a x a x ax a x a − − − − − − − − = − + + + + = + − + − + L L Quadratic Formula Solve 2 0ax bx c+ + = , 0a ≠ 2 4 2 b b acx a − ± − = If 2 4 0b ac− > - Two real unequal solns. If 2 4 0b ac− = - Repeated real solution. If 2 4 0b ac− < - Two complex solutions. Square Root Property If 2x p= then x p= ± Absolute Value Equations/Inequalities If b is a positive number or or p b p b p b p b b p b p b p b p b = ⇒ = − = < ⇒ − < < > ⇒ < − > Completing the Square Solve 22 6 10 0x x− − = (1) Divide by the coefficient of the 2x 2 3 5 0x x− − = (2) Move the constant to the other side. 2 3 5x x− = (3) Take half the coefficient of x, square it and add it to both sides 2 2 2 3 3 9 293 5 5 2 2 4 4 x x    − + − = + − = + =        (4) Factor the left side 23 29 2 4 x − =    (5) Use Square Root Property 3 29 29 2 4 2 x − = ± = ± (6) Solve for x 3 29 2 2 x = ±