Answer:
The value of a is 16
Step-by-step explanation:
Given the product
[tex](y - 4)(y^2 + 4y + 16)[/tex]
we have to apply the distributive property express the expression in the form
[tex] y^3 + 4y^2 + ay - 4y^2 - ay - 64\text{ to find the value of a}[/tex]
By distributive property
[tex]a(b+c)=a.b+a.c[/tex]
[tex](y - 4)(y^2 + 4y + 16)[/tex]
[tex]y(y^2 + 4y + 16)-4(y^2 + 4y + 16)[/tex]
[tex]y^3+4y^2+16y-4y^2-16y-64[/tex]
[tex]\text{Compare this equation with }y^3 + 4y^2 + ay - 4y^2 - ay - 64[/tex]
gives a=16
hence, the value of a is 16
