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

I got a =16.
Hope this helps! :D

Answer 2

The value of a is 16

Explanation:

Given the product

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

we have to apply the distributive property express the expression in the form

`y^3 + 4y^2 + ay - 4y^2 - ay - 64\text{ to find the value of a}`

By distributive property

`a(b+c)=a.b+a.c`

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

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

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

`\text{Compare this equation with }y^3 + 4y^2 + ay - 4y^2 - ay - 64`

gives a=16

hence, the value of a is 16