Question

select the correct answer.

what is the simplest form of this expression?

\\((2x - 3)(3x^2 + 2x - 1)\\)

\\(6x^3 - 5x^2 - 6x + 2\\)
\\(6x^3 - 9x^2 - 4x + 3\\)
\\(6x^3 - 5x^2 - 8x + 3\\)
\\(6x^3 - 2x^2 - 8x + 3\\)

Explanation:

Distribute the terms of the binomial

$$ (2x - 3)(3x^2 + 2x - 1) = 2x(3x^2 + 2x - 1) - 3(3x^2 + 2x - 1) $$

Expand each distributed term

$$ 2x(3x^2 + 2x - 1) = 6x^3 + 4x^2 - 2x $$

$$ -3(3x^2 + 2x - 1) = -9x^2 - 6x + 3 $$

Combine like terms to simplify

$$ (6x^3 + 4x^2 - 2x) + (-9x^2 - 6x + 3) = 6x^3 + (4 - 9)x^2 + (-2 - 6)x + 3 = 6x^3 - 5x^2 - 8x + 3 $$

Answer:

• (A) \(6x^3 - 5x^2 - 6x + 2\)
• (B) \(6x^3 - 9x^2 - 4x + 3\)
• (C) \(6x^3 - 5x^2 - 8x + 3\) (Correct answer)
• (D) \(6x^3 - 2x^2 - 8x + 3\)