Ank'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?

Question

Sienna Sweeney

Mathematics

5 March, 10:54

Ank'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?

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Braelyn Norris · Answer 1

Using the distributive property to obtain the product we shall have:

(y - 3) (y2 + 3y + 9)

=y (y2 + 3y + 9) - 3 (y2 + 3y + 9)

=y^3+3y^2+9y-3y^2-9y-27

putting like terms together:

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

=y^3+0y^2+0y-27

=y^3-27

From above bold expression the value of a is: a=9