Answer :
To simplify the expression [tex](2x)^3 \cdot x - 2x^2[/tex], we can break it down into steps:
Simplify [tex](2x)^3[/tex]:
Raise [tex]2x[/tex] to the power of 3.
[tex](2x)^3 = (2^3)(x^3) = 8x^3[/tex]
Multiply [tex]8x^3[/tex] by [tex]x[/tex]:
Multiply the result from the previous step by [tex]x[/tex].
[tex]8x^3 \cdot x = 8x^{3+1} = 8x^4[/tex]
Subtract [tex]2x^2[/tex] from [tex]8x^4[/tex]:
Subtract [tex]2x^2[/tex] from the expression.
Since the terms [tex]8x^4[/tex] and [tex]2x^2[/tex] have different powers, they cannot be combined, but it helps to write both terms clearly:
[tex]8x^4 - 2x^2[/tex]
Thus, simplifying the expression does not directly match any given options as a direct simplification. However, if we assume the need to compare to approximate terms or possible errors in multiple-choice options, we could focus on if rewriting or example determines a typographic disclosure. None directly rewrite into given terms in choices as verified. No selection among A, B, C, D merges or parallels by allocation alternative yet reflects identified equation state for accurately presented terms. Keep in check for checks; adjustments identify assignments as composite renovation shown yet placeholder reflective without reduced connection so correct maintain is text independent, essentially & essentially isolate, detail isn’t listings reflected.
