Find the difference between two polynomial expressions.

1. Distribute the negative sign: The problem requires finding the difference between two polynomials. This means we need to subtract the second polynomial from the first. The subtraction sign in front of the second parenthesis means we distribute a -1 to each term inside that parenthesis.
$$(0.4k^3 - 2.5k) - (2.4k^3 + 3k^2 - 1.2k)$$
$$= 0.4k^3 - 2.5k - 1 \cdot (2.4k^3) - 1 \cdot (3k^2) - 1 \cdot (-1.2k)$$
$$= 0.4k^3 - 2.5k - 2.4k^3 - 3k^2 + 1.2k$$

2. Group like terms: To simplify, we group terms with the same variable and exponent together.
$$= (0.4k^3 - 2.4k^3) + (-3k^2) + (-2.5k + 1.2k)$$

3. Combine like terms: Perform the addition and subtraction for each group of like terms.
For the $k^3$ terms: $0.4k^3 - 2.4k^3 = -2.0k^3$
For the $k^2$ terms: $-3k^2$
For the $k$ terms: $-2.5k + 1.2k = -1.3k$

4. Write the final simplified expression: Combine the results from the previous step.
$$-2.0k^3 - 3k^2 - 1.3k$$