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?

As we can see in his simplification there are 2 pairs of terms that negate each other because of oposite sign which will leave us with y^3 - 27 which is indeed difference of cubes.

we can notice that first he multiplied y from binomial with each term in trinomial. third multiplication is y*9 which means that a = 9

Answer is 9