(a+b)^2 =a^2 +b^2 +2ab (a+b+c)^2 =a^2 +b^2 +c^2 +2ab+2bc+2ca (a+b+c+d)^2 =? (a_1 +a_2 +...+a_n )^2 =? Derive a formula or give a technique.


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Question Number 2196 by Rasheed Soomro last updated on 08/Nov/15

${(a + b)}^{2} = a^{2} + b^{2} + 2 a b$ ${(a + b + c)}^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$ ${(a + b + c + d)}^{2} = ?$ ${(a_{1} + a_{2} + . . . + a_{n})}^{2} = ?$ $D e r i v e a f o r m u l a o r g i v e a t e c h n i q u e .$
	Answered by 123456 last updated on 08/Nov/15

	${(a_{1} + \cdot \cdot \cdot + a_{n})}^{k} = \sum_{α_{1} \cdot \cdot \cdot α_{n}} (\begin{matrix} k \\ α_{1}, \cdot \cdot \cdot α_{n} \end{matrix}) a_{1}^{α_{1}} \cdot \cdot \cdot a_{n}^{α_{n}}$ $Σ α_{n} = k, α_{i} \in N, k \in N$ $(\begin{matrix} α \\ α_{1}, \cdot \cdot \cdot, α_{n} \end{matrix}) = \frac{α!}{α_{1}! \cdot \cdot \cdot α_{n}!}$
	Commented by 123456 last updated on 08/Nov/15

	$multinomial coeficients and multinomil$ $expansion$
	Commented by Rasheed Soomro last updated on 08/Nov/15

	$W h a t a r e α_{i} ? F o r e x a m p l e f o r {(a_{1} + a_{2} + a_{3} + a_{4})}^{3} w h a t$ $a r e α_{i} ?$
	Commented by 123456 last updated on 08/Nov/15

	$the possible natural pars such that$ $α_{1} + \cdot \cdot \cdot + α_{n} = k$ $α_{i} \in N$
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