A 3 - b 3 - c 3 can be written using - notation as -

Given: a^3+b^3+c^3 It can be written as: ∑ _ a,b,c ^ #160; a ^ 3 ...

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Sum of n Terms

a 3 + b 3 + c...

Question

$a^{3} + b^{3} + c^{3}$ can be written using $\sum$ notation as _____ .

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Solution

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a^{3} + b^{3} + c^{3} - 3 a b c

x^{3} + y^{3} + z^{3} - 3 x y z

A^{3} + B^{3} + C^{3} - 3 A B C

a^{3} (b - c)^{3} + b^{3} (c - a)^{3} + c^{3} (a - b)^{3}

a^{3} {(b - c)}^{3} + b^{3} {(c - a)}^{3} + c^{3} {(a - b)}^{3}

{(a + b + c)}^{3} - a^{3} - b^{3} - c^{3} = 3 (a + b) (b + c) (c + a)

{(a + b + c)}^{3} - a^{3} - b^{3} - c^{3} = [{(a + b + c)}^{3} - a^{3}] - [b^{3} + c^{3}]

\frac{a^{3}}{b^{3}} + \frac{b^{3}}{c^{3}} + \frac{c^{3}}{a^{3}} - 3

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