Answer:
Option: D is the correct answer.
The product is:
D. [tex]a^6-64[/tex]
Step-by-step explanation:
We are asked to simplify the given algebraic expression i.e. we have to find the product of two algebraic expressions, which are a polynomial in terms of "a"
As both are cubic polynomial so there product will be a six-degree polynomial.
( Since on multiplying the degree gets add up )
The expression is as follows:
[tex](a^3+8)(a^3-8)[/tex]
We know that:
[tex](a+b)(a-b)=a^2-b^2[/tex]
Hence we get the product as:
[tex](a^3+8)(a^3-8)=(a^3)^2-(8)^2\\\\\\i.e.\\\\\\(a^3+8)(a^3-8)=a^6-64[/tex]
Hence, the product is:
[tex]a^6-64[/tex]
