Simplifying the Expression (a b)(2a-3b c)-(2a-3b) c

To simplify the given expression, we will follow the rules of algebra and apply the distributive property, combine like terms, and perform any necessary operations.

Step 1: Distribute the first term (a b) to the second term (2a-3b c):

(a b)(2a-3b c) = 2a^2 b - 3ab^2 c

Step 2: Multiply the result from Step 1 by -1 and c:

-1(2a^2 b - 3ab^2 c) = -2a^2 b + 3ab^2 c

Step 3: Distribute the third term (2a-3b) to c:

(2a-3b) c = 2ac - 3bc

Step 4: Subtract the result from Step 3 from the result from Step 2:

(-2a^2 b + 3ab^2 c) - (2ac - 3bc)

Step 5: Combine like terms:

-2a^2 b + 3ab^2 c - 2ac + 3bc

Step 6: Rearrange the terms:

-2a^2 b - 2ac + 3ab^2 c + 3bc

Final Answer: The simplified form of the expression (a b)(2a-3b c)-(2a-3b) c is -2a^2 b - 2ac + 3ab^2 c + 3bc.

Explanation:
- In the given expression, we have two terms: (a b) and (2a-3b c).
- To simplify the expression, we first distribute the first term (a b) to the second term (2a-3b c) using the distributive property.
- The result of the first step is 2a^2 b - 3ab^2 c.
- Next, we multiply the result from Step 1 by -1 and c to get -2a^2 b + 3ab^2 c.
- Then, we distribute the third term (2a-3b) to c, resulting in 2ac - 3bc.
- Finally, we subtract the result from Step 3 from the result of Step 2 and combine like terms to get the final simplified expression: -2a^2 b - 2ac + 3ab^2 c + 3bc.