Algebraic Formulae Flashcards
Products, exponents, and logarithms
x^2 - y^2
(x + y)(x - y)
x^3 +/- y^3
(x +/- y)(x^2 -/+ xy + y^2)
(x +/- y)^2
x^2 +/- 2xy + y^2
(x +/- y)^3
x^3 +/- 3x^2y + 3xy^2 +/- y^3
x^0
1, if x does not = 0
x^1
x
x^-n
1/x^n if x does not = 0
x^m . x^n
x^(m+n)
(x^m)^n
x^(mn)
x^m / x^n
x^(m-n) if x does not = 0
(x.y)^m
x^m . y^m
(x/y)^n
x^n / x^y
x^(m/n)
nrt(x^m) if a is >/= 0, m>/= 0, n >/= 0
y = log(a)x
x = a^y where a>0, a does not = 0
a^(log(a)M)
m
log(a)M^x
xlog(a)M
log(a)(M.N)
log(a)M + log(a)N
log(a)(M/N)
log(a)M - log(a)N
log(a)M
log(b)M/log(b)a = logM/loga = lnM/lna = log(10)M/log(10)a
log(a)a
1 if a>0
log(a)1
0 if a>0
log(e)x
lnx
ln(xy)
lnx + lny
ln(x/y)
lnx - lny
lnx^y
ylnx
lne^x
x if x>0
e^(lnx)
x
lne
1
ln1
0
e^x = e^y
x = y
lnx = lny
x = y
a^b = z
lnz = blna –> b = lnz/lna
a^(lnb)
b^(lna)
(a/b)/(c/d)
ad/bc
Quadratic Equation
ax^2 + bx + c = 0, where a, b, c are constants and a does not equal 0.
Quadratic Formula
[-b +/- sqrt(b^2 - 4ac)]/2a = x (root)
Inverse
f(g(x)) = x, then g(x) = f^(-1)(x). Switch x and y.
