SpecialProductsExamples 125

Question

Factor $64k^{3} + l^{3}$

Answer

$\;\;\;64k^{3} + l^{3}$

$=(4k)^3 + (l)^3$

$=A^3 + B^3 \text{ , where } A = 4k \text{ and } B = l$

$=(A + B)(A^2 - AB + B^2)$

$=(4k + l)((4k)^2 - (4k)(l) + (l)^2)$

$=(4k + l)(16k^{2} - 4kl +l^{2})$