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

Answer:

The value of a is 16    

Step-by-step 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