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MATH (ALGEBRA)

math algebra

ALGEBRAIC IDENTITIES


1.   (a + b)2 = a2 + 2ab + b2
2.   (a − b)2 = a2 − 2ab + b2
3.   (a + b)2 + (a − b)2 = 2(a2 + b2)
4.   (a + b)2 − (a − b)2 = 4ab
5.   (a + b)3 = a3 + b3 +3ab (a+ b)
6.   (a − b)3 = a3 − b3 − 3ab (a − b)
7.   (a2− b2) = (a + b) (a − b)
8.   (a3 + b3) = (a + b) (a2 − ab + b2)
9.   (a3 − b3) = (a − b) (a2+b2 +ab)
10.   (a + b+ c)2 = a2 + b2 + c2+2(ab + bc + ca)
11.   (a – b − c)2 = a2 + b2 +c2 − 2(ab + ac − bc)
12.   (a + b + c)3 = a3 + b3 + c3 +3(a+b) (b+c) (c+a)
13.   (a3 + b3 + c3 – 3abc) = (a+b+c) (a2+b2+c2 − ab−bc −ca)
If a + b + c = 0 then, a3 + b3 + c3 = 3abc

         15.  x3+y3=(x+y) (x2xy+y2)

           16.  x3y3=(xy) (x2+xy+y2)

           17.  x2+y2+z2xyyzzx=1/2[(xy)2+(yz)2+(zx)2]




1.   Laws of Exponents (am)(an) = am+n (ab)m = amb(am)n = amn

2.   Fractional Exponents 

a.   a0 = 1 
b.   am/an=amn 
c.   am = 1/am 
d.   am = 1/am








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