Confused by negative sign and exponents

Question

This is starting to get ridiculous but I need help.

I have this:
$7\left(5^p-2^{p+1}\right)-10\left(5^{p-1}-2^p\right)$

And I'm trying to get to this:
$5^p\left(7-2\right)-2^p\left(14-10\right)$

Somehow I'm confusing myself when I'm trying to work with these numbers. Could someone please walk me through this?

Thanks!

Answer 1

we have $$7(5^p-2^{p+1})-5\cdot 2(5^{p-1}-2^p)=5^p(7-2)+2^{p+1}(5-7)$$

Answer 2

$$7\left(5^p-2^{p+1}\right)-10\left(5^{p-1}-2^p\right)$$ $$= 7(5^p) - 7(2^{p+1}) - 10(5^{p-1}) + 10(2^p)$$ $$ =7(5^p) - 7(2^{p+1}) - 2(5^{p}) + 5(2^{p+1})$$ $$ 5^p(7-2) - 2^{p+1}(7 - 5)$$