ALGEBRA

Algebra

Algebra is a branch of mathematics that uses mathematical statements to describe relationships between things that vary over time.

Factoring Formulas

Real numbers : a, b, c
Natural number : n

1. a2 – b2 = ( a + b)(a – b )
2. a3 – b3 = ( a – b )(a2 + ab + b2)
3.  a3 + b3 = ( a + b )(a2 - ab + b2)
4.  a4 – b4 = (a2 – b2)( a2 + b2) = ( a + b)(a – b ) )( a2 + b2)
5.  a5 – b5 = ( a – b)(a4 + a3b + a2b2 + ab3 + b4)
6.  a5 + b5 = ( a + b)(a4 - a3b + a2b2 - ab3 + b4)
7.  If n is odd, then an + bn = ( a + b)(an-1 – an-2b + an-3b2 - … - abn-2 + bn-1).
8.  If n is even, then an – bn = ( a - b)(an-1 + an-2b + an-3b2 + … + abn-2 + bn-1).
an + bn = ( a + b)(an-1 – an-2b + an-3b2 - … + abn-2 - bn-1).

Product Formulas
Real numbers : a, b, c
Whole numbers : n, k
9.       ( a – b )2 = a2 – 2ab + b2
10.     ( a + b )2 = a2 + 2ab + b2
11.     ( a – b )3 = a3 – 3a2b + 3ab2 – b3
12.     ( a + b )3 = a3 + 3a2b + 3ab2 + b3
13.     ( a – b )4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4
14.     ( a + b )4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
15.     Binomial Formula
( a + b )n = nC0an + nC1an-1b + nC2an-2b2 + … + nCn-1abn-1 + nCn-1bn,
16.     ( a + b + c )2 = a2 + b2 + c2 + 2ab + 2ac + 2bc
17.     ( a + b + c + … + u + v )2 = a2 + b2 + c2 + … + u2 + v2 +
+ 2 ( ab + ac + … + au + av + bc + … + bu + bv + … + uv )