To simplify the expression \((7x^2 + 13x - 19) - (4x + 7 - 16x^2)\), we will first distribute the negative sign across the terms in the parentheses.
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Start with the original expression:
\[ (7x^2 + 13x - 19) - (4x + 7 - 16x^2) \]
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Distribute the negative sign:
\[ 7x^2 + 13x - 19 - 4x - 7 + 16x^2 \]
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Combine like terms:
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Combine \(7x^2\) and \(16x^2\): \[ 7x^2 + 16x^2 = 23x^2 \]
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Combine \(13x\) and \(-4x\): \[ 13x - 4x = 9x \]
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Combine \(-19\) and \(-7\): \[ -19 - 7 = -26 \]
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So the simplified expression is:
\[ 23x^2 + 9x - 26 \]
Thus, the final answer is:
\[ \boxed{23x^2 + 9x - 26} \]