Question

factor $6z^5 - 750z^2$ completely.
$6z^5 - 750z^2 = \square$

Explanation:

Step1: Factor out GCF

Identify and factor the greatest common factor of $6z^5$ and $750z^2$, which is $6z^2$.
$6z^5 - 750z^2 = 6z^2(z^3 - 125)$

Step2: Recognize difference of cubes

Notice $z^3 - 125$ is a difference of cubes ($a^3 - b^3$ where $a=z$, $b=5$).
$z^3 - 125 = z^3 - 5^3$

Step3: Apply difference of cubes formula

Use the difference of cubes identity $a^3 - b^3=(a-b)(a^2+ab+b^2)$.
$z^3 - 5^3=(z-5)(z^2+5z+25)$

Step4: Combine all factors

Substitute the factored form back into the expression from Step1.
$6z^2(z-5)(z^2+5z+25)$

Answer:

$6z^2(z-5)(z^2+5z+25)$