Question

1. 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. $24y^{3}+10y^{2}+51y + 35$

Explanation:

Step1: Distribute $6y$ to each term

$6y \times 4y^2 + 6y \times (-3y) + 6y \times (-5) = 24y^3 - 18y^2 - 30y$

Step2: Distribute $7$ to each term

$7 \times 4y^2 + 7 \times (-3y) + 7 \times (-5) = 28y^2 - 21y - 35$

Step3: Combine all resulting terms

$24y^3 - 18y^2 - 30y + 28y^2 - 21y - 35$

Step4: Combine like terms

$24y^3 + (-18y^2+28y^2) + (-30y-21y) - 35 = 24y^3 + 10y^2 - 51y - 35$

Answer:

c. $24y^{3}+10y^{2}-51y-35$