Page 31 - Standard Handbook Of Petroleum & Natural Gas Engineering

20 Mathematics
Rules of Multiplication and Simple Factoring

a*b=b*a

(ab)c = a(bc)
a(b + c) = ab + ac

a(-b) = -ab and -a(- b) = ab
(a + b)(a - b) = a2 - b2

(a + b)2 = a2 + 2ab + b2
and

(a - b)2 = a2 - 2ab + b2
(a + b)s = a3 + 3a2 + 3ab2 + bS
and

(a - b)s = a3 - 3a2 + 3ab2 - bs

(For higher order polynomials see the section “Binomial Theorem”)
a” + b” is factorable by (a + b) if n is odd, thus
a3 + b” = (a + b)(a2 - ab + b2)

and a” - b” is factorable by (a - b), thus
a” - b” = (a - b)(a”-’ + a”- 2b + . . . + abn-2 + bn-1 1

Fractions
The numerator and denominator of a fraction may be multiplied or divided
by any quantity (other than zero) without altering the value of the fraction, so
that, if m # 0,

ma+mb+mc - a+b+c
-
mx+my X+Y
To add fractions, transform each to a common denominator and add the
numerators (b,y # 0):

To multiply fractions (denominators # 0):