Question

DISTRIBUTIVE PROPERTY Use the distributive property to rewrite the expression without parentheses. $$ -2 t(12-t) $$

Short answer

The given expression \(-2t(12 - t)\) simplified using the distributive property is \(2t^2 - 24t\).

Step-by-step solution

Identify the components

The given expression is \(-2t(12 - t)\). Here, -2t is like 'a', while (12 - t) is like a sum of 'b' and 'c' where 'b' is 12 and 'c' is -t.

Apply the Distributive Property - Part 1

First, multiply 'a' which is -2t with 'b' which is 12. This gives the product -24t.

Apply the Distributive Property - Part 2

Next, multiply 'a' which is -2t with 'c' which is -t. This gives the product 2t^2.

Combine the Results

Combine both the products -24t and 2t^2. Since they're not like terms, they can't be simplified further. Therefore, the expression \(-2t(12 - t)\) is equivalent to \(2t^2 - 24t\) when the distributive property is applied.