Question

using the distributive property to find the product $(y - 4x)(y^{2} + 4y + 16)$ results in a polynomial of the form $y^{3} + 4y^{2} + ay - 4xy^{2} - axy - 64x$. what is the value of $a$ in the polynomial?
32
8
4
16

Explanation:

Step1: Distribute $y$ to the trinomial

$y(y^2 + 4y + 16) = y^3 + 4y^2 + 16y$

Step2: Distribute $-4x$ to the trinomial

$-4x(y^2 + 4y + 16) = -4xy^2 - 16xy - 64x$

Step3: Combine the two products

$(y^3 + 4y^2 + 16y) + (-4xy^2 - 16xy - 64x) = y^3 + 4y^2 + 16y - 4xy^2 - 16xy - 64x$

Step4: Match with given polynomial form

Compare to $y^3 + 4y^2 + ay - 4xy^2 - axy - 64x$ to identify $a$.

Answer:

16