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? 3 9 18 27.

Answer 1

The value of a is 9, the correct option is B.

Given

Hank’s teacher asked him to verify that the product (y−3)(y2+3y+9), is a difference of cubes.

Quadratic equation;

The equation which has the highest degree is 2 is called quadratic equation;

$\rm ax^2+bx+c=0$

Where a, b, and c are the constants.

The given polynomial is;

$\rm (y-3)(y^2+3y+9)$

On multiplying the terms;

$\rm (y-3)(y^2+3y+9)\\\\y(y^2+3y+9)-3(y^2+3y+9)\\\\y^3+3y^2+9y-3y^2-9y-27$

On comparing;

$\rm ay = 9y\\\\a=9$

Hence, the value of a is 9.

To know more about polynomial click the link is given below.

brainly.com/question/6169816