To subtract the polynomial expressions \( (3x^5 + 7x^2 - 4x + 8) - (4x^4 + 8x^2 - 3x + 7) \), we need to distribute the negative sign across the second expression and combine like terms.
Starting with the given expression:
\[ (3x^5 + 7x^2 - 4x + 8) - (4x^4 + 8x^2 - 3x + 7) \]
Distributing the negative sign:
\[ = 3x^5 + 7x^2 - 4x + 8 - 4x^4 - 8x^2 + 3x - 7 \]
Now, we can combine like terms:
- For \( x^5 \): \( 3x^5 \)
- For \( x^4 \): \( -4x^4 \)
- For \( x^2 \): \( 7x^2 - 8x^2 = -1x^2 \) (or \(-x^2\))
- For \( x \): \( -4x + 3x = -1x \) (or \(-x\))
- Constant terms: \( 8 - 7 = 1 \)
Putting it all together, we get:
\[ 3x^5 - 4x^4 - x^2 - x + 1 \]
Thus, the simplified result of the subtraction is:
\[ \boxed{3x^5 - 4x^4 - x^2 - x + 1} \]
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