Answer:
product y ³ - 64 and a = 16.
Step-by-step explanation:
Given : (y — 4)(y² + 4y + 16) .
To find : Using the distributive property to find the product a polynomial of the form y³ + 4y² + ay – 4y² – ay – 64. What is the value of a in the polynomial?
Solution : We have given
(y — 4)(y² + 4y + 16) .
Distribute y over (y² + 4y + 16) and - 4 over (y² + 4y + 16).
y (y² + 4y + 16) - 4 (y² + 4y + 16).
y ³+ 4y² + 16 y - 4y² - 16y - 64.
This is in form of y³ + 4y² + ay – 4y² – ay – 64.
Here, a = 16.
Product : combine like terms
y ³+ 4y² - 4y² + 16y - 16y - 64.
y ³ - 64.
Therefore , product y ³ - 64 and a = 16.
