Combining like terms

[Dillinger4]

Ive been having trouble understanding how to combine like terms when multiplication is distributed over addition. If anyone could help it would be great. Two problems that i have banging my head over are the following

4(2x³ + x²) - 5x²
= 8x³ - x² 'books answer

I end up getting 8x³ + 4x² - 5x²


Here is another one..... 3(5c) - 15c² + c
-15c² + 16c 'books answer

Now 3 * 5c would give us 15c.

15c - 15c² or 15c + (-15c²)

should gives us 0 c¹ which boils down to c

so i end up with c + c.