Factor completely 12 z squared minus 75 z to the fourth power

Answer: 3z^2 (2+5z) (2-5z)

Step-by-step explanation:

12 z^2 - 75 z^4

To factor this, you'd want to find the GCF, which is 3 z^2, and factor it out.

3 z^2 (4 - 25 z^2)

Rewrite (4 - 25 z^2) in the form a^2 - b^2, where a=2 and b=5z.

3z^2 (2^2 - (5z) ^2)

Use the "Difference of two squares": a^2 - b^2 = (a+b) (a-b)

3z^2 (2+5z) (2-5z)