Question

Using the distributive property to find the product (y – 4)(y2 + 4y + 16) results in a polynomial of the form y3 + 4y2 + ay – 4y2 – ay – 64. What is the value of a in the polynomial?

Answer 1

For this case we have the following expression:

`(y - 4) (y ^ 2 + 4y + 16)`

Using the distributive property, we have:

`y (y ^ 2 + 4y + 16) -4 (y ^ 2 + 4y + 16)`

Rewriting the expression we have:

`y^ 3 + 4y ^ 2 + 16y - 4y ^ 2 - 16y - 64`

Comparing with the given expression we have:

`y ^ 3 + 4y ^ 2 + ay - 4y ^ 2 - ay - 64 = y ^ 3 + 4y ^ 2 + 16y - 4y ^ 2 - 16y - 64`

From where we conclude that:

`a = 16`

Answer:

The value of a in the polynomial is:

`a = 16`

Answer 2

(y - 4)(y^2 + 4y + 16) = y^3 + 4y^2 + 16y - 4y^2 - 16y - 64

Therefore, a = 16.