Special Products Rule 6

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Expand $(11u + v)(121u^{2} - 11uv +v^{2})$

**Answer**

$\;\;\;(11u + v)(121u^{2} - 11uv +v^{2})$

$=(11u + v)((11u)^2 - (11u)(v) + (v)^2) $

$=(A + B)(A^2 - AB + B^2) \text{ , where } A = 11u \text{ and } B = v $

$=A^3 + B^3 $

$=(11u)^3 + (v)^3 $

$=1331u^{3} + v^{3} $