To subtract the two expressions \((4x^3 - 5x^2 + 4)\) and \((4x^3 - 2x^2 + 7x)\), we follow these steps:
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Distribute the negative sign to the second expression: \[ (4x^3 - 5x^2 + 4) - (4x^3 - 2x^2 + 7x) = 4x^3 - 5x^2 + 4 - 4x^3 + 2x^2 - 7x \]
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Combine like terms:
- The \(4x^3\) terms cancel each other: \[ 4x^3 - 4x^3 = 0 \]
- The \(x^2\) terms combine: \[ -5x^2 + 2x^2 = -3x^2 \]
- The \(x\) term: \[ -7x \]
- The constant term: \[ 4 \]
Putting it all together, we get: \[ 0 - 3x^2 - 7x + 4 \] which simplifies to: \[ -3x^2 - 7x + 4 \]
Thus, the result of the subtraction is: \[ -3x^2 - 7x + 4 \]