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Simplify the expression (x - 2)(-2x² - 4x + 6). Explain your answer.

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Final answer:

To simplify the expression (x - 2)(-2x² - 4x + 6), multiply each term in the first expression by each term in the second expression and combine like terms. The simplified expression is -2x³ - 2x - 12.

Step-by-step explanation:

To simplify the expression (x - 2)(-2x² - 4x + 6), we can use the distributive property. Multiply each term in the first expression, x - 2, by each term in the second expression, -2x² - 4x + 6, and then combine like terms.

Let's multiply:

  • x * -2x² = -2x³
  • x * -4x = -4x²
  • x * 6 = 6x
  • -2 * -2x² = 4x²
  • -2 * -4x = 8x
  • -2 * 6 = -12

Now let's combine like terms:

  • -2x³ + 4x² + 6x - 4x² - 8x - 12
  • -2x³ + (4x² - 4x²) + (6x - 8x) -12
  • -2x³ - 2x - 12

So, the simplified expression is -2x³ - 2x - 12.

User Frank Kalis
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