Special Products Rule 7

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Expand $(9k - l)(81k^{2} + 9kl +l^{2})$

**Answer**

$\;\;\;(9k - l)(81k^{2} + 9kl +l^{2})$

$=(9k - l)((9k)^2 + (9k)(l) + (l)^2) $

$=(A - B)(A^2 + AB + B^2) \text{ , where } A = 9k \text{ and } B = l $

$=A^3 - B^3 $

$=(9k)^3 - (l)^3 $

$=729k^{3} - l^{3} $