SOLUTION: Please simplify (2b-2)(4b²-2b-5)

Please simplify
(2b-2)(4b²-2b-5)

There are 2 terms in the first parentheses and 3 terms in the second
parentheses.  Since 2×3 = 6 we expect to get 6 terms after multiplying
and before simplifying

1. Multiply the term 2b in the first parentheses
   by 4b² in the second parentheses. That gives 8b³.

So far we have 8b³

2. Multiply the term 2b in the first parentheses
   by -2b in the second parentheses. That gives -4b².

So far we have 8b³ - 4b²

3. Multiply the term 2b in the first parentheses
   by -5 in the second parentheses. That gives -10b.

So far we have 8b³ - 4b² - 10b

4. Multiply the term -2 in the first parentheses
   by 4b² in the second parentheses. That gives -8b².

So far we have 8b³ - 4b² - 10b - 8b²

5. Multiply the term -2 in the first parentheses
   by -2b in the second parentheses. That gives +4b.

So far we have 8b³ - 4b² - 10b - 8b² + 4b

6. Multiply the term -2 in the first parentheses
   by -5 in the second parentheses. That gives +10.

We have 8b³ - 4b² - 10b - 8b² + 4b + 10
       
That's 6 terms, so we have done all the multiplying required.

Now we must simplify by combining like terms:

To keep things straight, draw one line under each
term in b², and two lines under each term in b. Be
sure to underline their signs too: 

8b³ - 4b² - 10b - 8b² + 4b + 10
          ¯¯¯¯¯       ¯¯¯¯
Now combine the terms with one line under them, getting -12b², and
combine the terms with two lines under them, getting -6b.

So the final answer is

8b³ - 12b² - 6b + 10

Edwin