To simplify the expression \((7x + 1)(-7x)(2x - 3)\), we can follow these steps:
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First, simplify the product of the first two factors, \((7x + 1)(-7x)\): \[ (7x + 1)(-7x) = -7x(7x) - 7x(1) = -49x^2 - 7x \]
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Next, we will multiply this result by the third factor \((2x - 3)\): \[ (-49x^2 - 7x)(2x - 3) \]
We will use the distributive property to multiply each term in \(-49x^2 - 7x\) by each term in \(2x - 3\):
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First, multiplying \(-49x^2\) by \(2x\): \[ -49x^2 \cdot 2x = -98x^3 \]
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Next, multiplying \(-49x^2\) by \(-3\): \[ -49x^2 \cdot -3 = 147x^2 \]
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Now, multiplying \(-7x\) by \(2x\): \[ -7x \cdot 2x = -14x^2 \]
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Finally, multiplying \(-7x\) by \(-3\): \[ -7x \cdot -3 = 21x \]
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Now we combine all the products: \[ -98x^3 + 147x^2 - 14x^2 + 21x \]
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Combine like terms: \[ -98x^3 + (147x^2 - 14x^2) + 21x = -98x^3 + 133x^2 + 21x \]
Thus, the simplified expression is: \[ \boxed{-98x^3 + 133x^2 + 21x} \]