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

Multiply your (y - 4)(y^2 + 4y + 16) to determine a:
(y)(y^2) + (y)(4y) + (y)(16) - (4)(y^2) - (4)(4y) - (4)(16)
y^3 + 4y^2 + 16y - 4y^2 - 16y - 64
As you can see, a there is 16. That's the answer.
Hope this helps!

Answer 2

a = 16

Explanation:

Given : Using the distributive property to find the product
`\left(y\:-4\right)\left(y^2+4y\:+16\right)` results in a polynomial of the form
`y^3+4y^2 + ay-4y^2-ay-64.`

We have to find the value of a in the polynomial.

Consider the product of
`\left(y\:-4\right)\left(y^2+4y\:+16\right)`

Using distributive property, Multiply each term of first bracket with each term of second bracket.

We get,

`\left(y\:-4\right)\left(y^2+4y\:+16\right)=y(y^2+4y+16)-4(y^2+4y+16)\\\\\\ \left(y\:-4\right)\left(y^2+4y\:+16\right)=yy^2+y\cdot \:4y+y\cdot \:16 \left(-4\right)y^2+\left(-4\right)\cdot \:4y+\left(-4\right)\cdot \:16`

Simplify , we get,

`=y^2y+4yy+16y-4y^2-4\cdot \:4y-4\cdot \:16`

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

Thus, comparing with
`y^3 + 4y^2 + ay-4y^2-ay-64.` , we get a = 16