Answer:
Option d) [tex](4-x^5)(16+x^{10}+4x^5)[/tex]
Step-by-step explanation:
We are given the following in the question.
[tex]64-x^{15}[/tex]
We have to factorize the given expression.
Using the algebraic identity:
[tex]a^3 - b^3 = (a-b)(a^2+b^2+ab) = (a-b)^3 +3ab(a-b)[/tex]
[tex]64-x^{15}\\\\(4)^3 - (x^5)^3\\\\(4 - x^5)(4^2 + (x^5)^2 + 4x^5)\\\\(4-x^5)(16+x^{10}+4x^5)[/tex]
Hence, the factors of given expression is given by option d) [tex](4-x^5)(16+x^{10}+4x^5)[/tex]
