Short Answer 
The simplified product of the expression ((b-2c)(-3b+c)) has a degree of 2 and contains exactly 2 negative terms. The final result, after applying the distributive property and combining like terms, is (-3b^2 + 7bc – 2c^2).
Step 1: Expand the Expression
To begin simplifying the expression ((b-2c)(-3b+c)), we apply the distributive property (also known as the FOIL method for binomials). This involves multiplying each term in the first binomial by each term in the second binomial. The multiplication process includes:
- Multiply (b) by (-3b) to yield (-3b^2).
- Multiply (b) by (c) to yield (bc).
- Multiply (-2c) by (-3b) to yield (6bc).
- Multiply (-2c) by (c) to yield (-2c^2).
Step 2: Combine Like Terms
Next, we combine the results of our previous multiplication to simplify the expression further. The result will involve gathering terms that have the same degree. This includes:
- From (-3b^2), we have one distinct term.
- From (bc + 6bc), we can combine these to get (7bc).
- Lastly, (-2c^2) remains as is since it has no like terms.
Step 3: Analyze the Resulting Expression
After combining like terms, the simplified expression is (-3b^2 + 7bc – 2c^2). Analyze the final result to determine key characteristics:
- The highest degree of the resulting polynomial is (2), confirming that it has a degree of (2).
- There are a total of three terms in the expression, with two of them (-3b^2) and (-2c^2) being negative.
Thus, the expressions confirm the correct options as C and E.