Step-by-step answer:
First, we need to understand the rule of exponents.
When powers of a particular variable are multiplied, the exponents add.
For example, x^3*x^4 = x^(3+4) = x^7 ......................(1)
When there is a division, the exponents subtract.
For example, y^5/y^3 = y^(5-3) = y^2 ....................(2)
Also, the distributive property says
p*(q+r+s) = pq + pr + ps ......................(3)
Using the above basic rules, we have
-a^2b^2c^2*( a + b - c )...................... use (3) to distribute
= -a^2b^2c^2*a -a^2b^2c^2*b + a^2b^2c^2*c..................use (1) to multiply
= -a^3b^2c^2 -a^2b^3c^2 + a^2b^2c^3