Question

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

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

1. what is $(v - 3)(5v^{2}+3v + 5)$?

○ a. $5v^{3}-12v^{2}-5v - 14$
○ b. $5v^{3}-12v^{2}-4v + 15$
○ c. $5v^{3}-12v^{2}-4v - 15$
○ d. $5v^{3}-11v^{2}-4v - 15$

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

○ a. $24n^{3}-14n^{2}-51n - 8$
○ b. $24n^{3}-15n^{2}-51n - 8$
○ c. $24n^{3}-14n^{2}-49n - 7$
○ d. $24n^{3}-14n^{2}-51n + 8$

Explanation:

Step1: Expand first product via FOIL

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

Step2: Combine like terms

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

Step3: Expand second product via distributive property

$(v-3)(5v^2+3v+5) = v(5v^2+3v+5) -3(5v^2+3v+5)$
$= 5v^3 +3v^2 +5v -15v^2 -9v -15$

Step4: Combine like terms

$5v^3 + (3v^2-15v^2) + (5v-9v) -15$
$= 5v^3 -12v^2 -4v -15$

Step5: Expand third product via distributive property

$(6n+1)(4n^2-3n-8) = 6n(4n^2-3n-8) +1(4n^2-3n-8)$
$=24n^3 -18n^2 -48n +4n^2 -3n -8$

Step6: Combine like terms

$24n^3 + (-18n^2+4n^2) + (-48n-3n) -8$
$=24n^3 -14n^2 -51n -8$

Answer:

1. c. $5m^3+5m^2-12m-4$
2. c. $5v^3 -12v^2 -4v -15$
3. a. $24n^3 -14n^2 -51n -8$