Question

1. what is $(m + 2)(5m^{2}-5m - 2)?$

a. $5m^{3}+5m^{2}-11m - 3$
b. $5m^{3}+5m^{2}-12m - 4$
c. $5m^{3}+5m^{2}-12m - 5$
d. $5m^{3}+6m^{2}-12m - 4$

Explanation:

Step1: Distribute $(m+2)$

$(m+2)(5m^2 - 5m - 2) = m(5m^2 - 5m - 2) + 2(5m^2 - 5m - 2)$

Step2: Expand each term

$m(5m^2 - 5m - 2) = 5m^3 - 5m^2 - 2m$
$2(5m^2 - 5m - 2) = 10m^2 - 10m - 4$

Step3: Combine like terms

$5m^3 - 5m^2 - 2m + 10m^2 - 10m - 4 = 5m^3 + (-5m^2+10m^2) + (-2m-10m) - 4$
$= 5m^3 + 5m^2 - 12m - 4$

Answer:

b. $5m^3 + 5m^2 - 12m - 4$