Question

1. what is $(8m - 3)(3m^{2} - 6m - 4)?$

a. $23m^{3} - 57m^{2} + 14m + 12$
b. $24m^{3} - 57m^{2} - 14m + 12$
c. $24m^{3} - 57m^{2} - 14m + 11$
d. $24m^{3} + 56m^{2} - 14m + 11$

Explanation:

Step1: Distribute $8m$ to each term

$8m \times 3m^2 + 8m \times (-6m) + 8m \times (-4)$
$=24m^3 - 48m^2 - 32m$

Step2: Distribute $-3$ to each term

$-3 \times 3m^2 + (-3) \times (-6m) + (-3) \times (-4)$
$=-9m^2 + 18m + 12$

Step3: Combine all resulting terms

$24m^3 - 48m^2 - 32m -9m^2 + 18m + 12$

Step4: Combine like terms

$24m^3 + (-48m^2-9m^2) + (-32m+18m) + 12$
$=24m^3 -57m^2 -14m +12$

Answer:

b. $24m^{3}-57m^{2}-14m+12$