Question about Distribution

[zhkhelpneeded]

This was originally a calculus problem, but the part that I'm stuck on is the algebra part.

Essentially, the problem is take the derivative of y = 3t(2t^2-5)^5

From this, I got 3(2t^2-5)^5 + 3t(20t [ 2t^2-5]^4 using the product rule (f'g + fg')

When I tried to simplify this, I got 3(2t^2 - 5)^4 * (22t^2-5) but the answer is :



I am stumped at how it arrived to that answer with (2t^2 - 5)^4 being the same. How come the 3 was also distributed to one part and not the other?

Which part am I missing? What topics can I review to better understand this concept?
I would like to know how to approach this fully by hand.

 

[mikegonz00]

So you got y'=3(2t²-5)⁵+60t²(2t-5)⁴ after using the product rule and simplifying a bit right?
Then to get to the solution you have there as a picture, just factor out (2t²-5)⁴.
Then, y' = (2t²-5)⁴(3(2t²-5)+60t²) = (66t²-15)(2t²-5)⁴.

If you're still having trouble, it can be useful to use a substitution like 2t²-5 = u, simplify, and then plug back in the original expression