Square Formulas
 (a + b) ^{ 2 } = a ^{ 2 } + b ^{ 2 } + 2ab
 (a − b) ^{ 2 } = a ^{ 2 } + b ^{ 2 } − 2ab
 a ^{ 2 } − b ^{ 2 } = (a − b) (a + b)
 (x + a) (x + b) = x ^{ 2 } + (a + b) x + ab
 (a + b + c) ^{ 2 } = a ^{ 2 } + b ^{ 2 } + c ^{ 2 } + 2ab + 2bc + 2ca

(a + (−b) + (−c))
^{
2
}
= a
^{
2
}
+ (−b)
^{
2
}
+ (−c)
^{
2
}
+ 2a (−b) + 2 (−b) (−c) + 2a (−c)
(a – b – c) ^{ 2 } = a ^{ 2 } + b ^{ 2 } + c ^{ 2 } − 2ab + 2bc − 2ca
Cube Formulas
 (a + b) ^{ 3 } = a ^{ 3 } + b ^{ 3 } + 3ab(a + b)
 (a − b) ^{ 3 } = a ^{ 3 }  b ^{ 3 }  3ab(a  b)
 a ^{ 3 } − b ^{ 3 } = (a − b) (a ^{ 2 } + b ^{ 2 } + ab)
 a ^{ 3 } + b ^{ 3 } = (a + b) (a ^{ 2 } + b ^{ 2 } − ab)
 (a + b + c) ^{ 3 } = a ^{ 3 } + b ^{ 3 } + c ^{ 3 } + 3(a + b)(b + c)(c + a)
 a ^{ 3 } + b ^{ 3 } + c ^{ 3 } − 3abc = (a + b + c) (a ^{ 2 } + b ^{ 2 } + c ^{ 2 } − ab − bc − ac)

If (a + b + c) = 0,
a ^{ 3 } + b ^{ 3 } + c ^{ 3 } = 3abc
Some not so Common Formulas
Power n Formula
 a ^{ n } − b ^{ n } = (a − b) (a ^{ n−1 } + a ^{ n−2 } b ^{ 1 } + a ^{ n−3 } b ^{ 2 } + .... + a ^{ 1 } b ^{ n−2 } + b ^{ n−1 } )
Exponent Law
View

√a = a ^{ 1/2 }

∛a = a ^{ 1/3 }

^{ n } √a = a ^{ 1/n }
 a ^{ p. } a ^{ q } = a ^{ p + q }
 a ^{ p } / a ^{ q } = a ^{ p  q }
 a ^{ p. } b ^{ p } = (ab) ^{ p }
 (a ^{ p } ) ^{ q. } = a ^{ pq }
 a ^{ 0 } ^{ . } = 1
 a ^{ –n. } = 1/a ^{ n }
For Irrational Numbers
Quadratic Formula