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?

a=16

Step-by-step explanation:

Given

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

To find the value of a in the resulting polynomial we have to solve the given expression

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

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

To find the value of a, both the polynomials will be compared

y^3+4y^2+16y-4y^2-16y-64  

y^3+4y^2+ay-4y^2-ay-64

Comparing the coefficients of both polynomials gives us that

a=16

So, the value of a is 16 ..