<s>[INST] About $(x^3 - 4)^2 - x^6 + 2x^5 = 2x^5 -8x^3 + 16$ Studying polynomials I got the follows:
$$
    (x^3 - 4)^2 - x^6 + 2x^5 = 2x^5 -8x^3 + 16
$$
I can't understand from where we got this $-8x^3$.
I got to simplify this polynomial just to:
$$
2x^5 + 16
$$
Can someone help me understand from where we got the expression $-8x^3$ ?
 [/INST] When expanding $(x^3-4)^2$, you get $x^6-4x^3-4x^3+16=x^6-8x^3+16.$ Then, the $x^6$ is subtracted off, and you are left with $2x^5-8x^3+16$, as desired. 
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