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

(y - 4)(y² + 4y + 16)

y³ + 4y² + 16y - 4y² -16y - 64

y³ + 4y² + ay - 4y² - ay - 64

a = 16

Answer 2

16

Explanation:

Since this is a multiplication of the square of (y+4) by (y-4) the value of Y will be eliminated in the product, if you want to assure this you just need to do the multiplication, and to do so we just need to multiply feach factor in the binomial by the polynomial:

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

So now we know that the value for the Y is 16.