608 moleswobth’s pocket-book
Algebraic Fokmulæ (from ‘ Algebra Self-taught,’ Dr. Paget Higgs).
Addition and Subtraction. n + ( - m) = n - m = — (m - n)-'
n - (+ m) = n + (-m); n - (- m) = n + (+ m) = n + ’
Multiplication. a.b - a x b — a b; n Cm + p) = nm + np ■
(— ri) X (— m) = + m n; (+ ri) (— m) = — mn.
Division. a + b=^ = a.b-, (-a): (-&) = a := +
(-a):(+?>) = (+a)b) = ® ± «.
bp p p
mn m n p n n
— = — . n = m. - ; — = - : w = -: m.
P P p mn m n
Fkactions. “ = =
b bn b:n b b b ’
a n__an an a p ap
b p bp’ b ' p~ b ‘ n~ bn'
Powers and Roots. am . bm — (a b)m ; am: bM = ;
am. an _ am + n; am-.an = am “ “ ; (a™)“ = amn ;
(- a)2n — a2n ; (_ a)2n + I — _ a2n + 1 ; (« ± (,)2 — a2 2 a b + b^-
(a ± 6)3 — a3 ± 3 b + 3 a b^ ± b3 ; n°=l; a —00 = either 0 or «>;
= —a- = ”/a;
“Ä/a ,^/b = ’li/ab; a; \/b = */an = .
VVä= m^;2^a=±b;
2 nJ - * = ± bV^i; 2m+^Ta = + Ci 2™+^rtt = _ c.
Logarithms, log, m n = log. m + log. n; log. — = log. m - log. n;
l og. = m log. X ; log. ^7= Ä.
‘lit
Equations. Let x ± m = n, then x = n^m. Let n x = m, then x =—.
a? n
• Let — = mt then x — n m. Let — — m. then x ~ ~ •
n x m
Let xn = m, then x X/m. Let ^Jx = m, then x = m" .
Let ax — b, then x log. a = log. b, and x = —•
log. a