Special Products Rule 4

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Expand $(4a + b)^3 $

**Answer**

$\;\;\;(4a + b)^3 $

$=(A + B)^3 \text{ , where } A = 4a \text{ and } B= b$

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

$=(4a)^3 + 3(4a)^2(b) + 3(4a)(b)^2 + (b)^3 $

$= 64a^{3} + 3(16a^{2})(b) + 3(4a)(b^{2}) + b^{3} $

$= 64a^{3} + 48a^{2}b + 12ab^{2} + b^{3} $