How to simplify recurrence relation?

Question

I'm having trouble seeing how

$$5(2^{n-1} + 5\cdot 3^{n-1}) - 6(2^{n-2} + 5\cdot3^{n-2})$$

simplifies to:

$$2^{n-2}\cdot (10 - 6) + 3^{n-2} \cdot (75 - 30)$$

How can I simplify the above expression to get to the second version?

Answer 1

hint: $$5\cdot 2^{n-1} = 5\cdot 2\cdot 2^{n-2} = 10\cdot 2^{n-2}, 5\cdot 3^{n-1} = 5\cdot 3\cdot 3^{n-2} = 15\cdot 3^{n-2}$$, and combine like terms.