Special Products Rule 5

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Expand $(3x - y)^3 $

**Answer**

$\;\;\;(3x - y)^3 $

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

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

$=(3x)^3 - 3(3x)^2(y) + 3(3x)(y)^2 - (y)^3 $

$= 27x^{3} - 3(9x^{2})(y) + 3(3x)(y^{2}) - y^{3} $

$= 27x^{3} - 27x^{2}y + 9xy^{2} - y^{3} $