Question

what is $(8m - 3)(3m^{2}-6m - 4)?$
a. $24m^{3}-57m^{2}-14m + 12$
b. $23m^{3}-57m^{2}+14m + 12$
c. $24m^{3}+56m^{2}-14m + 11$
d. $24m^{3}-57m^{2}-14m + 11$

what is $(6y + 7)(4y^{2}-3y - 5)?$
a. $24y^{3}-10y^{2}+51y - 35$
b. $24y^{3}+10y^{2}-51y - 35$
c. $24y^{3}+10y^{2}+51y + 35$
d. $24y^{3}-10y^{2}-51y + 35$

what is $(n - 1)(6n - 6)?$
a. $6n^{2}-12n + 5$
b. $6n^{2}-12n + 6$
c. $6n^{2}-14n + 7$
d. $6n^{2}-10n + 6$

Explanation:

Step1: Expand first product

Multiply each term:
$$(8m-3)(3m^2-6m-4) = 8m(3m^2-6m-4) -3(3m^2-6m-4)$$
$$=24m^3-48m^2-32m-9m^2+18m+12$$
Combine like terms:
$$=24m^3+(-48m^2-9m^2)+(-32m+18m)+12$$
$$=24m^3-57m^2-14m+12$$

Step2: Expand second product

Multiply each term:
$$(6y+7)(4y^2-3y-5) = 6y(4y^2-3y-5)+7(4y^2-3y-5)$$
$$=24y^3-18y^2-30y+28y^2-21y-35$$
Combine like terms:
$$=24y^3+(-18y^2+28y^2)+(-30y-21y)-35$$
$$=24y^3+10y^2-51y-35$$

Step3: Expand third product

Multiply each term:
$$(n-1)(6n-6) = n(6n-6)-1(6n-6)$$
$$=6n^2-6n-6n+6$$
Combine like terms:
$$=6n^2+(-6n-6n)+6$$
$$=6n^2-12n+6$$

Answer:

1. a. $24m^3 - 57m^2 - 14m + 12$
2. b. $24y^3 + 10y^2 - 51y - 35$
3. b. $6n^2 - 12n + 6$