using the distributive property to find the product $(y - 4x)(y^{2}+4y + 16)$ results in a polynomial of the…

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?\n4\n8\n16\n32

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?\n4\n8\n16\n32

Answer

Explanation:

Step1: Expand the product ((y - 4x)(y^{2}+4y + 16)) using the distributive property (FOIL - First, Outer, Inner, Last for binomial - polynomial multiplication).

[ \begin{align*} (y-4x)(y^{2}+4y + 16)&=y\times(y^{2}+4y + 16)-4x\times(y^{2}+4y + 16)\ &=y^{3}+4y^{2}+16y-4xy^{2}-16xy-64x \end{align*} ]

Step2: Compare the expanded form (y^{3}+4y^{2}+16y-4xy^{2}-16xy - 64x) with the given form (y^{3}+4y^{2}+ay-4xy^{2}-axy-64x).

By comparing the coefficients of the (y) - terms ((16y)) and (xy) - terms ((-16xy)) with (ay) and (-axy) respectively.

Answer:

C. 16