Answer:
Factor of [tex]64-x^{15}[/tex] is [tex](4-x^{5})(16+4x^{5}+x^{10})[/tex]
Step-by-step explanation:
We need to factor the expression [tex]64-x^{15}[/tex]
Re-write the given expression [tex]64-x^{15}[/tex] as;
[tex]4^{3}-(x^{5})^{3}[/tex]
Since, [tex]a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})[/tex]
so, here [tex]a = 4[/tex] and [tex]b = x^{5}[/tex]
[tex](4-x^{5})(4^{2}+4x^{5}+(x^{5})^{2})[/tex]
[tex](4-x^{5})(16+4x^{5}+x^{10})[/tex]
Hence, factor of [tex]64-x^{15}[/tex] is
[tex](4-x^{5})(16+4x^{5}+x^{10})[/tex]
