Special Products Rule 4

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Expand $(2u + v)^3 $

**Answer**

$\;\;\;(2u + v)^3 $

$=(A + B)^3 \text{ , where } A = 2u \text{ and } B= v$

$=A^3 + 3A^2B + 3AB^2 + B^3 $

$=(2u)^3 + 3(2u)^2(v) + 3(2u)(v)^2 + (v)^3 $

$= 8u^{3} + 3(4u^{2})(v) + 3(2u)(v^{2}) + v^{3} $

$= 8u^{3} + 12u^{2}v + 6uv^{2} + v^{3} $