Question

which expression is equivalent to ((2k^2 - 3m)(3k - 4))?
options:
(6k^3 - 8k^2 - 9km + 12m)
(6k^3 + 12m)
(-2k^3 + 3km)
(-2k^2 - 9km - 12m)

Explanation:

Step1: Apply distributive property

We need to expand \((2k^2 - 3m)(3k - 4)\) using the distributive property (FOIL method).
First, multiply \(2k^2\) by \(3k\): \(2k^2\times3k = 6k^3\)
Then, multiply \(2k^2\) by \(-4\): \(2k^2\times(-4)=-8k^2\)
Next, multiply \(-3m\) by \(3k\): \(-3m\times3k=-9km\)
Finally, multiply \(-3m\) by \(-4\): \(-3m\times(-4) = 12m\)

Step2: Combine the terms

Now, combine all the terms we got from the distributive property:
\(6k^3-8k^2 - 9km+12m\)

Answer:

\(6k^3 - 8k^2 - 9km + 12m\) (corresponding to the option with this expression)