To subtract the polynomial expressions \((3x^5 + 7x^2 - 4x + 8) - (4x^4 + 8x^2 - 3x + 7)\), we first distribute the negative sign across the second polynomial:
\[ 3x^5 + 7x^2 - 4x + 8 - 4x^4 - 8x^2 + 3x - 7 \]
Next, we can combine like terms. We will align the terms according to their degrees:
- The \(x^5\) term: \(3x^5\)
- The \(x^4\) term: \(-4x^4\)
- The \(x^2\) terms: \(7x^2 - 8x^2 = -1x^2\) (or \(-x^2\))
- The \(x\) terms: \(-4x + 3x = -1x\) (or \(-x\))
- The constant terms: \(8 - 7 = 1\)
Putting it all together, we have:
\[ 3x^5 - 4x^4 - x^2 - x + 1 \]
Thus, the simplified result of the polynomial subtraction is:
\[ \boxed{3x^5 - 4x^4 - x^2 - x + 1} \]
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