Answer: The product of -a²b²c²(a+b-c) is:
-a³b²c² - a²b³c² + a²b²c³
Step-by-step explanation: o find the product of the expression -a²b²c²(a+b-c), we can follow these steps:
1. Distribute the -a²b²c² across the terms inside the parentheses (a+b-c):
-a²b²c²(a) + (-a²b²c²)(b) + (-a²b²c²)(-c)
2. Simplify each term by multiplying the coefficients and combining like terms:
-a³b²c² - a²b³c² + a²b²c³
Let's break down each term:
Term 1: -a³b²c²
- The exponent of 'a' is 3 because we have a coefficient of -a² and one 'a' from the distribution.
- The exponent of 'b' is 2 because we have a coefficient of -a² and two 'b's from the distribution.
- The exponent of 'c' is 2 because we have a coefficient of -a² and two 'c's from the distribution.
Term 2: -a²b³c²
- The exponent of 'a' is 2 because we have a coefficient of -a² and no additional 'a's from the distribution.
- The exponent of 'b' is 3 because we have a coefficient of -a² and three 'b's from the distribution.
- The exponent of 'c' is 2 because we have a coefficient of -a² and two 'c's from the distribution.
Term 3: a²b²c³
- The exponent of 'a' is 2 because we have a coefficient of -a² and no additional 'a's from the distribution.
- The exponent of 'b' is 2 because we have a coefficient of -a² and two 'b's from the distribution.
- The exponent of 'c' is 3 because we have a coefficient of -a² and three 'c's from the distribution.
So, the product of -a²b²c²(a+b-c) is:
-a³b²c² - a²b³c² + a²b²c³
Please let me know if I can help you with anything else.
