What-is-the-general-rule-for-factorising-a-b-c-n-

Question Number 118937 by harckinwunmy last updated on 20/Oct/20

What is the general rule

for factorising {(a + b + c)}^{n} ?

Answered by mathmax by abdo last updated on 20/Oct/20

i think the question is developping

{(a + b + c)}^{n} = \sum_{k = 0}^{n} C_{n}^{k} {(a + b)}^{k} c^{n - k}

= \sum_{k = 0}^{n} C_{n}^{k} (\sum_{p = 0}^{k} C_{k}^{p} a^{p} b^{k - p}) c^{n + k}

= \sum_{k = 0}^{n} C_{n}^{n} \sum_{p = 0}^{k} C_{k}^{p} a^{p} b^{k - p} c^{n + k}