- a2 – b2 = (a – b)(a + b)
- (a + b)2 = a2 + 2ab + b2
- a2 + b2 = (a + b)2 – 2ab
- (a – b)2 = a2 – 2ab + b2
- (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
- (a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
- (a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
- (a – b)3 = a3 – 3a2b + 3ab2 – b3 = a3 – b3 – 3ab(a – b)
- a3 – b3 = (a – b)(a2 + ab + b2)
- a3 + b3 = (a + b)(a2 – ab + b2)
- (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
- (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4
- a4 – b4 = [{(a – b)(a + b)}(a2 + b2)]
- a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)
- If n be a natural number, then: an – bn = (a – b)(an-1 + an-2b+…...+ bn-2a + bn-1)
- If n is even number (n = 2k),then, an + bn = (a + b)(an-1 – an-2b +…...+ bn-2a – bn-1)
- If n is a odd number then, (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b +an-3b2…- bn-2a + bn-1)
- (a + b + c + …)2 = a2 + b2 + c2 + ...… + 2(ab + ac + bc + …...)
- Formula of Exponents: (am).(an) = am+n
- (ab)m = ambm
- (am)n = amn
a+b)n=an+nan−1b+n(n−1)2!an−2b2+n(n−1)(n−2)3!an−3b3+….+bn,where,n>1aman=am− 1a−ma − - Factorial function: (a+b)n=an+nan−1b+n(n−1)2!an−2b2+n(n−1)(n−2)3!an−3b3+..….+bn,where,n>1
