To simplify the expression \( 8x^3(3x - 4) \), you distribute \( 8x^3 \) to each term inside the parentheses:
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Multiply \( 8x^3 \) by \( 3x \): \[ 8x^3 \cdot 3x = 24x^4 \]
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Multiply \( 8x^3 \) by \( -4 \): \[ 8x^3 \cdot -4 = -32x^3 \]
Now, combine the results:
\[ 8x^3(3x - 4) = 24x^4 - 32x^3 \]
Thus, the simplified form of the expression is:
\[ \boxed{24x^4 - 32x^3} \]
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