To simplify the expression \(-4x^3(5x^2 + 2)\), you need to distribute \(-4x^3\) to both terms inside the parentheses.
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Multiply \(-4x^3\) by \(5x^2\): \[ -4x^3 \cdot 5x^2 = -20x^{3+2} = -20x^5 \]
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Multiply \(-4x^3\) by \(2\): \[ -4x^3 \cdot 2 = -8x^3 \]
Now, combine the results:
\[ -20x^5 - 8x^3 \]
Thus, the simplified form of the expression is:
\[ \boxed{-20x^5 - 8x^3} \]