SpecialProductsExample 123

Question

Expand $(u - v)^3 $

Answer

$\;\;\;(u - v)^3 $

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

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

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

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

$= u^{3} - 3u^{2}v + 3uv^{2} - v^{3} $