using the distributive property to find the product (y - 4x)(y²+4y + 16) results in a polynomial of the form…

using the distributive property to find the product (y - 4x)(y²+4y + 16) results in a polynomial of the form y³+4y²+ay - 4xy²-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)(y²+4y + 16) results in a polynomial of the form y³+4y²+ay - 4xy²-axy - 64x. what is the value of a in the polynomial?\n4\n8\n16\n32

Answer

Explanation:

Step1: Apply distributive property

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

Step2: Compare with given form

Comparing $y^{3}+4y^{2}+16y-4xy^{2}-16xy - 64x$ with $y^{3}+4y^{2}+ay-4xy^{2}-axy-64x$, we can see that $a = 16$.

Answer:

C. 16