Final answer:
The multiplication of the binomials (3T - T² - 3) and (1 - T) is performed using the FOIL method, resulting in the simplified answer 3T - 4T² + T³.
Therefore, the product of the given binomials is 3T - 4T² + T³.
Step-by-step explanation:
The question requires us to multiply two binomials: (3T - T² - 3) and (1 - T). To do this, we use the distributive property, also known as the FOIL method for binomials, which stands for First, Outer, Inner, Last.
First: Multiply the first terms in each binomial (3T * 1 = 3T).
Outer: Multiply the outer terms (3T * -T = -3T²).
Inner: Multiply the inner terms (-T² * 1 = -T²).
Last: Multiply the last terms (-T² * -T = T³).
Combine like terms (3T - 3T² - T² + T³).
Simplify to get the final answer 3T - 4T² + T³.
Therefore, the product of the given binomials is 3T - 4T² + T³.