Question

Hank’s teacher asked him to verify that the product (y – 3)(y2 + 3y + 9) is a difference of cubes. He used the distributive property to multiply the binomial times the trinomial. Before simplifying, his product was a polynomial of the form y3 + 3y2 + ay – 3y2 – ay – 27. What is the value of a in the polynomial?

Answer 1

Thank you

Answer 2

no prob

Answer 3

(y-3)(y^2 + 3y + 9)

distribute the y first

(y)(y^2 + 3y + 9) --> (y^3 + 3y^2 + 9y)

then distribute the -3

-3(y^2 + 3y + 9) ---> -3y^2 - 9y - 27

compare
(y^3 + 3y^2 + 9y) -3y^2 - 9y - 27

with

y3 + 3y2 + ay – 3y2 – ay – 27

to figure out what the a term would be