math expansions

D is given by a 1 1 A 1 1 + a 1 2 A 1 2 + a 1 3 A 1 3 This is first row expansion of the determinant. Similarly, we can expand the determinant along any row or any column. In general, where i = 1, 2 and 3 or Where j = 1, 2 and..

We shall discuss expansions of binomials and trinomi..

We shall discuss expansions of binomials, trinomials, Formulae 1. a 2 + b 2 = (a + b) 2 - 2ab 2. a 2 + b 2 = (a - b) 2 + 2ab 3. (a + b) 2 = (a - b) 2 + 4..

Expansions Summary - (a + b) 2 = a 2 + 2ab + b 2 (a + b) 2 = a 2 + 2ab + b 2 (a - b) 2 = a 2 - 2ab + b 2 In the above two formulae the middle term = (a + b) (a - b) = a 2 - b 2 (x + a) (x + b) = x 2 + (a + b)x + ab. (a + b + c) 2 = a 2 + b 2 + c 2 + 2ab + 2bc + 2ac (a + b) 3 = a 3 + b 3 +..

Some particular expansions for Positive Integral Index - For n N, we have: a) (a - b) n (a +(- b))..

The first term in the expansion of (a + b) n is n C 0 a n b 0 . For the second term, the coefficient is taken as n C 1 , the power of 'a' is decreased by one and the power of 'b' is increased by one. So, the second term is n C 1 a n - 1 b 1 . For the third term, the coefficien..

For n Q, we have: ..

Find the fifth term of the binomial expansion (3 - x ) 6 . => 105 x 5 or -135 x 4 or 235 x 5 or 135 x 4..

Find the coefficient of the term x 8 in the expansion of ( x - 4) 10 . => 740 or 680 or 700 or 720..

Find the eighth term in the binomial expansion of ( x - 2) 7 . => -512 or 64 or 256 or -128..