To perform the operation \((4-2x)(-6x^2 + 10x + 21 - 2x)\), we first need to simplify the inner expression.
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Simplify the expression inside the parentheses: \[ -6x^2 + 10x + 21 - 2x = -6x^2 + (10x - 2x) + 21 = -6x^2 + 8x + 21 \]
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Now we multiply \( (4-2x) \) with \( (-6x^2 + 8x + 21) \): Using the distributive property (FOIL method), we get: \[ (4)(-6x^2) + (4)(8x) + (4)(21) + (-2x)(-6x^2) + (-2x)(8x) + (-2x)(21) \]
Calculating each term: \[ -24x^2 + 32x + 84 + 12x^3 - 16x^2 - 42x \]
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Now, combine like terms:
- Combine the \(x^3\): \(12x^3\)
- Combine the \(x^2\): \(-24x^2 - 16x^2 = -40x^2\)
- Combine the \(x\): \(32x - 42x = -10x\)
- The constant term: \(84\)
So, by combining everything we have: \[ 12x^3 - 40x^2 - 10x + 84 \]
The step that was performed is now: \[ 12x^3 - 40x^2 - 10x + 84 \]
None of the provided options exactly match this result after the complete simplification. However, it appears there may have been an error in the options given, as the calculations here are consistent based on the operation requested.
If you could verify if the expression presented correctly or if there are additional details, that would be helpful.
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