Question

What is the factorization of g3 – 125?

Answer 1

$\bf \textit{difference of cubes} \\ \quad \\ a^3+b^3 = (a+b)(a^2-ab+b^2)\qquad (a+b)(a^2-ab+b^2)= a^3+b^3 \\ \quad \\ a^3-b^3 = (a-b)(a^2+ab+b^2)\qquad (a-b)(a^2+ab+b^2)= a^3-b^3 \\\\ -------------------------------\\\\ g^3-125\implies g^3-5^3\implies (g-5)(g^2+5g+5^2) \\\\\\ (g-5)(g^2+5g+25)$