Question

What is the factored form of 64g^3+8

Answer 1

$\bf \textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2)\qquad (a+b)(a^2-ab+b^2)= a^3+b^3 \\\\ a^3-b^3 = (a-b)(a^2+ab+b^2)\qquad (a-b)(a^2+ab+b^2)= a^3-b^3\\\\ -------------------------------\\\\ 64g^3+8\implies 4^3g^3+8\implies (4g)^3+2^3 \\\\\\ (4g+2)[(4g)^2-(4g)(2)+2^2]\implies (4g+2)[(4^2g^2)-8g+4] \\\\\\ (4g+2)(16g^2-8g+4)$