Question

factoring diff / sum of cubes (level 1)
this is the only question in this section.
question
factor ( b^3 - 64z^3 ) completely.
answer attempt 1 out of 2

Explanation:

Step1: Identify difference of cubes

Rewrite $b^3 - 64z^3$ as $b^3 - (4z)^3$, since $4^3=64$.

Step2: Apply difference of cubes formula

Use the formula $a^3 - c^3=(a - c)(a^2 + ac + c^2)$, where $a=b$, $c=4z$.
Expression: $(b - 4z)(b^2 + b(4z) + (4z)^2)$

Step3: Simplify the quadratic term

Expand and simplify the second factor.
Expression: $(b - 4z)(b^2 + 4bz + 16z^2)$

Answer:

$(b - 4z)(b^2 + 4bz + 16z^2)$