Special Products Rule 5

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Expand $(a - b)^3 $

**Answer**

$\;\;\;(a - b)^3 $

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

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

$=(a)^3 - 3(a)^2(b) + 3(a)(b)^2 - (b)^3 $

$= a^{3} - 3(a^{2})(b) + 3(a)(b^{2}) - b^{3} $

$= a^{3} - 3a^{2}b + 3ab^{2} - b^{3} $