Precalculus Cheat Sheet
Essential formulas and identities
Fractions, Rational Expressions
ˆ
a
b
·
c
d
=
ac
bd
ˆ
a
b
÷
c
d
=
a
b
·
d
c
ˆ
a
b
±
c
d
=
ad ± bc
bd
ˆ
a + b
c
=
a
c
+
b
c
Powers and Roots
ˆ am · an = am+n,
am
an
= am−n
ˆ (am)n = amn
ˆ (ab)n = anbn,
a
b
n
=
an
bn
ˆ a0 = 1, a−n =
1
an
ˆ n
√
am = am/n
ˆ
√
ab =
√
a ·
√
b,
a
b
=
√
a
√
b
Binomial Expansions
ˆ (a ± b)2 = a2 ± 2ab + b2
ˆ (a ± b)3 = a3 ± 3a2b + 3ab2 ± b3
ˆ a2 − b2 = (a − b)(a + b)
ˆ a3 ± b3 = (a ± b)(a2 ab + b2)
Logarithmic Properties
ˆ logb(xy) = logb x + logb y
ˆ logb
x
y
= logb x − logb y
ˆ logb(xr) = r logb x
ˆ logb b = 1, logb 1 = 0
ˆ Change of base: logb x =
loga x
loga b
ˆ logb( n
√
x) =
1
n
logb x