Show that $7(3(2)^k + 2(5)^k) - 10(3(2)^{k-1} + 2(5)^{k-1}) = 3(2)^{k+1} + 2(5)^{k+1}$ $7(3(2)^k + 2(5)^k) - 10(3(2)^{k-1} + 2(5)^{k-1}) = 3(2)^{k+1} + 2(5)^{k+1}$
The problem is part of a proof. If you could also talk me through your thought process for solving this problem, I would greatly appreciate it. I've played around with several things like trying to get everything in terms of $a^{k+1}$ but I'm having no luck. Thanks!

Assuming the missing right parenthesis goes at the end:
$$7(3(2)^k + 2(5)^k) - 10(3(2)^{k-1} + 2(5)^{k-1}) =\\21\cdot 2^k+14\cdot 5^k-30\cdot 2^{k-1} -20\cdot 5^{k-1}=\\ 21\cdot 2^k +14\cdot 5^k-15\cdot 2^k-4\cdot 5^k=\\ 6\cdot 2^k+10\cdot 5^k=\\3(2)^{k+1} + 2(5)^{k+1}$$
