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Calculate (x - 2) × (3x + 1) × (4x - 3) when x is a real number.

a) 12x^3 - 10x^2 - 2x
b) 12x^3 - 5x^2 - 2x
c) 12x^3 - 5x^2 + 2x
d) 12x^3 - 10x^2 + 2x

1 Answer

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Final answer:

Upon expanding the given expression (x - 2) × (3x + 1) × (4x - 3), none of the provided options a, b, c, or d is correct. The correct result of the expansion, obtained through step-by-step multiplication, is 12x³ - 29x² + 7x + 6.

Step-by-step explanation:

To calculate (x - 2) × (3x + 1) × (4x - 3) when x is a real number, we should use the distributive property of multiplication over addition, which means we will expand the expression step-by-step.

First, focus on multiplying the two binomials: (x - 2) × (3x + 1). This will give us:

  • x * 3x = 3x²
  • x * 1 = x
  • -2 * 3x = -6x
  • -2 * 1 = -2

Combining these terms gives us: 3x² + x - 6x - 2 = 3x² - 5x - 2.

Now we take 3x² - 5x - 2 and multiply it by the third binomial (4x - 3):

  • 3x² * 4x = 12x³
  • 3x² * (-3) = -9x²
  • -5x * 4x = -20x²
  • -5x * (-3) = 15x
  • -2 * 4x = -8x
  • -2 * (-3) = 6

Combine like terms to get the final result: 12x³ - 9x² - 20x² + 15x - 8x + 6 which simplifies to 12x³ - 29x² + 7x + 6.

Therefore, none of the options a, b, c, or d provided is the correct expansion.

User Dotariel
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