Formulae
Simplification
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 + 2ac + 2bc
(a + b + c)3 = a3 + b3 + c3 + 3(a + b)(b + c)(c + a)
a3 + b3 + c3- 3abc = (a + b+ c) (a2 + b2 + c2 - ab - ac - bc)
(a – b – c)2 = a2 + b2 + c2 – 2ab – 2ac + 2bc
(a + b)3 = a3 + 3a2b + 3ab2 + b3 (a + b)3 = a3 + b3+ 3ab(a + b)
(a – b)3 = a3 – 3a2b + 3ab2 – b3
a3 – b3 = (a – b)(a2 + ab + b2)
a3 + b3 = (a + b)(a2 – ab + b2)
(a + b)3 = a3 + 3a2b + 3ab2 + b3
(a – b)3 = a3 – 3a2b + 3ab2 – b3
(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 is a natural number, an – bn = (a – b)(an-1 + an-2b+…+ bn-2a + bn-1)
If n is even (n = 2k), an + bn = (a + b)(an-1 – an-2b +…+ bn-2a – bn-1)
If n is odd (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b +…- bn-2a + bn-1)
(a + b + c + …)2 = a2 + b2 + c2 + … + 2(ab + ac + bc + ….
Exercise : Simplification and Approximation MCQ Questions and Answers
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