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? (\bigcirc) 4 (\bigcirc) 8 (\bigcirc) 16 (\bigcirc) 32

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

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

Step4: Match with given polynomial form

Compare $16y -16xy$ to $ay -axy$, identify $a$.

Answer:

16