Question

multiplying a binomial by a binomial

which equals the product of \\((x - 3)(2x + 1)\\)?

\\(2x^2 - 7x - 3\\)
\\(2x^2 - 5x - 3\\)
\\(3x - 2\\)
\\(6x^2\\)

Explanation:

Apply the distributive property

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

Expand the terms

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

Combine like terms

$$ 2x^2 + (1 - 6)x - 3 = 2x^2 - 5x - 3 $$

Answer:

• (A) \(2x^2 - 7x - 3\)
• (B) \(2x^2 - 5x - 3\) (Correct answer)
• (C) \(3x - 2\)
• (D) \(6x^2\)