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MathFlare Cheat Sheet

Trigonometric Numbers

Angle Sin Cos Tan
30° 12 √3 ÷ 2 √3 ÷ 3
45° √2 ÷ 2 √2 ÷ 2 1
60° √3 ÷ 2 12 √3
90° 1 0 -

Absolute Value Properties

Property Solution
|x| = y+ x=y OR x=-y
|x| > y+ x>y OR x<-y
|x| < y+ -y

Root Properties

Property Solution
n√xn |x|
(n√x)n x
n√(m√x) nm√x
n√xn√y n√xy
n√xn√y nxy
n√x n√xnx
nm√xkm n√xk

Popular Identities

Simplified Expanded
(a + b)2 a2 + 2ab + b2
(a - b)2 a2 - 2ab + b2
(a + b)3 a3 + 3a2b + 3ab2 + b3
(a - b)3 a3 - 3a2b + 3ab2 - b3
(a + b)4 a4 + 4a3b + 6a2b2 + 4ab3 + b4
(a - b)4 a4 - 4a3b + 6a2b2 - 4ab3 + b4
a2 + b2 (a + b)2 - 2ab OR (a - b)2 + 2ab
a2 - b2 (a + b)(a - b)
a3 + b3 (a + b)(a2 - ab + b2) OR (a + b)3 - 3ab(a + b)
a3 - b3 (a - b)(a2 + ab + b2) OR (a - b)3 + 3ab(a - b)
a4 + b4 (a + b)4 - 2ab(2a2 + 2b2 + 3ab) OR (a - b)4 + 2ab(2a2 - 2b2 + 3ab)
a4 - b4 (a - b)(a + b)(a2 + b2)
a16 - b16 (a - b)(a + b)(a2 + b2)(a4 + b4)(a8 + b8)
(a + b + c)2 a2 + b2 + c2 + 2ab + 2bc + 2ac
(a - b + c)2 a2 + b2 + c2 - 2ab - 2bc + 2ac
(a + b - c)2 a2 + b2 + c2 + 2ab - 2bc - 2ac
(a - b - c)2 a2 + b2 + c2 - 2ab + 2bc - 2ac

Popular Factorials

Number n Factorial n!
0! 1
1! 1
2! 2
3! 6
4! 24
5! 120
6! 720
7! 5,040
8! 40,320
9! 362,880
10! 3,628,800

Powers of 10

Exponent Number
Negative n-m
10-20 0.00000000000000000001
10-19 0.0000000000000000001
10-18 0.000000000000000001
10-17 0.00000000000000001
10-16 0.0000000000000001
10-15 0.000000000000001
10-14 0.00000000000001
10-13 0.0000000000001
10-12 0.000000000001
10-11 0.00000000001
10-10 0.0000000001
10-9 0.000000001
10-8 0.00000001
10-7 0.0000001
10-6 0.000001
10-5 0.00001
10-4 0.0001
10-3 0.001
10-2 0.01
10-1 0.1
Positive nm
100 1
101 10
102 100
103 1,000
104 10,000
105 100,000
106 1,000,000
107 10,000,000
108 100,000,000
109 1,000,000,000
1010 10,000,000,000
1011 100,000,000,000
1012 1,000,000,000,000
1013 10,000,000,000,000
1014 100,000,000,000,000
1015 1,000,000,000,000,000
1016 10,000,000,000,000,000
1017 100,000,000,000,000,000
1018 1,000,000,000,000,000,000
1019 10,000,000,000,000,000,000
1020 100,000,000,000,000,000,000