To rewrite the expression \((-29 - 10x^2 + 12x) + 3x(5x - 4)\) with the fewest terms possible, we will first distribute the \(3x\) in the second part of the expression and then combine like terms.
- Distribute \(3x\) to \(5x - 4\):
\[ 3x(5x - 4) = 15x^2 - 12x \]
- Substitute this back into the original expression:
\[ (-29 - 10x^2 + 12x) + (15x^2 - 12x) \]
- Combine like terms:
- For \(x^2\) terms: \(-10x^2 + 15x^2 = 5x^2\)
- For \(x\) terms: \(12x - 12x = 0\)
- The constant term remains: \(-29\)
- Write the final result:
The equivalent expression with the fewest terms possible is:
\[ 5x^2 - 29 \]
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