Final answer:
To simplify the given expression, distribute the terms and combine like terms, resulting in a simplified expression of -10x² + 21x - 12.
Step-by-step explanation:
To simplify the expression −4x(6x−4) + 5x − (12−14x²), we need to distribute and combine like terms. Start by expanding the terms within the parentheses:
- -4x(6x) = -24x²
- -4x(-4) = +16x
- 5x is already simplified and remains as it is
- Distribute the negative sign in front of the parenthesis (-): -12 + 14x²
So, the expression becomes:
-24x² + 16x + 5x - 12 + 14x²
Now, combine like terms:
- Combine the x² terms: -24x² + 14x² = -10x²
- Combine the x terms: 16x + 5x = 21x
- The constant term -12 remains as it is
The simplified expression is -10x² + 21x - 12.
Always remember to eliminate terms wherever possible to simplify the algebra and check the answer to ensure it is reasonable.