Algebraic Formulae Flashcards
Products, exponents, and logarithms
1
Q
x^2 - y^2
A
(x + y)(x - y)
2
Q
x^3 +/- y^3
A
(x +/- y)(x^2 -/+ xy + y^2)
3
Q
(x +/- y)^2
A
x^2 +/- 2xy + y^2
4
Q
(x +/- y)^3
A
x^3 +/- 3x^2y + 3xy^2 +/- y^3
5
Q
x^0
A
1, if x does not = 0
6
Q
x^1
A
x
7
Q
x^-n
A
1/x^n if x does not = 0
8
Q
x^m . x^n
A
x^(m+n)
9
Q
(x^m)^n
A
x^(mn)
10
Q
x^m / x^n
A
x^(m-n) if x does not = 0
11
Q
(x.y)^m
A
x^m . y^m
12
Q
(x/y)^n
A
x^n / x^y
13
Q
x^(m/n)
A
nrt(x^m) if a is >/= 0, m>/= 0, n >/= 0
14
Q
y = log(a)x
A
x = a^y where a>0, a does not = 0
15
Q
a^(log(a)M)
A
m
16
Q
log(a)M^x
A
xlog(a)M
17
Q
log(a)(M.N)
A
log(a)M + log(a)N
18
Q
log(a)(M/N)
A
log(a)M - log(a)N
19
Q
log(a)M
A
log(b)M/log(b)a = logM/loga = lnM/lna = log(10)M/log(10)a
20
Q
log(a)a
A
1 if a>0
21
Q
log(a)1
A
0 if a>0
22
Q
log(e)x
A
lnx
23
Q
ln(xy)
A
lnx + lny
24
Q
ln(x/y)
A
lnx - lny
25
lnx^y
ylnx
26
lne^x
x if x>0
27
e^(lnx)
x
28
lne
1
29
ln1
0
30
e^x = e^y
x = y
31
lnx = lny
x = y
32
a^b = z
lnz = blna --> b = lnz/lna
33
a^(lnb)
b^(lna)
34
(a/b)/(c/d)
ad/bc
35
Quadratic Equation
ax^2 + bx + c = 0, where a, b, c are constants and a does not equal 0.
36
Quadratic Formula
[-b +/- sqrt(b^2 - 4ac)]/2a = x (root)
37
Inverse
f(g(x)) = x, then g(x) = f^(-1)(x). Switch x and y.
