Question

what is ((y - 5)(y^2 - y + 8))?
a. (y^3 - 6y^2 + 13y - 40)
b. (y^3 - 6y^2 + 12y - 39)
c. (y^3 - 5y^2 + 13y - 40)
d. (y^3 - 6y^2 + 13y - 30)

Explanation:

Step1: Distribute $y$ to the trinomial

$y(y^2 - y + 8) = y^3 - y^2 + 8y$

Step2: Distribute $-5$ to the trinomial

$-5(y^2 - y + 8) = -5y^2 + 5y - 40$

Step3: Combine all terms

$y^3 - y^2 + 8y - 5y^2 + 5y - 40$

Step4: Combine like terms

$y^3 + (-y^2 -5y^2) + (8y +5y) -40 = y^3 -6y^2 +13y -40$

Answer:

a. $y^3 - 6y^2 + 13y - 40$