Factoring algebraic expressions- basic

Question

I would like to know the process of factoring this algebraic expression: 1) $64a^6+16a^3+1$

Thank you in advance!

Answer 1

set $$a^3=t$$ and factor $$64t^2+16t+1$$

Answer 2

Let $u = a^3$. Then $$64a^6 + 16a^3 + 1 = 64u^2 + 16u + 1 = (8u + 1)^2 = (8a^3 + 1)^2$$ Now use the sum of cubes formula $$x^3 + y^3 = (x + y)(x^2 - xy + y^2)$$ to factor the term inside the parentheses.