Expansions
We shall discuss expansions of binomials and trinomi..
Expansions
In algebra we come across certain products very frequently. For e.g., (a + b) 2 , (a + b) 3 (a + b + c) 2 etc. These are nothing but products of binomials or trinomials. We derive the formulae for these products and apply them whenever necessary. These expansions help..
Expansions
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..
Expansion of Gases
Expansion of Gases - Gases also expand on heating. Their volume expansion is very much greater than that of liquids. If a gas is heated at constant pressure, its volume increases and if a gas is heated at constant volume, its pressure increases due to expansion. Simila..
Binomial Theorem
Introduction - A binomial is an algebraic expression of two terms which are connected by the operations '+' or '-'. For n = 1,2,3,4, the expansion of (a + b) n , has been expressed in a very systematical manner in terms of combinatorial coefficients. The above expression suggest..
Introduction - A binomial is an algebraic expression of two terms which are connected by the operations '+' or '-'. For n = 1,2,3,4, the expansion of (a + b) n , has been expressed in a very systematical manner in terms of combinatorial coefficients. The above expression suggest..Expansions
Summary - (a + b) (a - b) = a 2 - b 2 (x + a) (x + b) = x 2 + (a + b)x + ab. (a + b) 3 = a 3 + b 3 + 3ab (a + b) = a 3 + 3a 2 b + 3ab 2 + b 3..
Binomial Theorem for Fractional Index
Binomial Theorem for Fractional Index - For any rational number n, We accept this expansion without proof. The restriction on x is not required when n is a natural number. Now, we shall see that when n is a natural number, then the above expansion coincides with that a..
Binomial Theorem for Fractional Index - For any rational number n, We accept this expansion without proof. The restriction on x is not required when n is a natural number. Now, we shall see that when n is a natural number, then the above expansion coincides with that a..Binomial Theorem Summary
of (a + b) n and is given by - If n is an odd natural number, then there are two middle terms in the expansion of (a + b)n and are given by i) The sum of all binomial coefficients in the expansion of (1+x) n is 2 n . ii) The sum of all even binomial coefficie..
of (a + b) n and is given by - If n is an odd natural number, then there are two middle terms in the expansion of (a + b)n and are given by i) The sum of all binomial coefficients in the expansion of (1+x) n is 2 n . ii) The sum of all even binomial coefficie..Use binomial theorem to find the expansion of (1 - x)5
Use binomial theorem to find the expansion of (1 - x) 5 => 1 - 5x + 10x 2 - 10x 3 - 5x 4 + x 5 or 1- x + x 2 - x 3 + x 4 - x 5 or 1 - 5x + 10x 2 - 10x 3 + 5x 4 - x 5 or 1- x 5..
Approximate (0.99)30 to the nearest tenth using the first two terms of..
Approximate (0.99) 30 to the nearest tenth using the first two terms of a binomial expansion. => 0.03 or 0.3 or 0.07 or 0.7..
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