Question

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?

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