Answer: The last option.
Step-by-step explanation:
1. You must square the binomial [tex](4x^{4}-3x^{2})^{2}[/tex]. By definition, you have:
[tex](a-b)^{2}=a^{2}-2ab+b^{2}[/tex]
2. Therefore:
[tex]9x^{5}+3x[(4x^{4})^{2}-2(4x^{4})(3x^{2})+(3x^{2})^{2}]=9x^{5}+3x[16x^{8}-24x^{6}+9x^{4}]=9x^{5}+48x^{9}-72x^{7}+27x^{5}[/tex]
3. When you add like terms, you obtain the following result:
[tex]48x^{9}-72x^{7}+36x^{5}[/tex]
4. Therefore, the answer is the last option.
