Question

multiply the polynomials.

\\((2g+3)(2g+3)\\)

• \\(2g^2 + 12g - 9\\)
• \\(4g^2 + 12g + 9\\)
• \\(2g^2 + 6g + 9\\)
• \\(4g^2 + 6g + 9\\)

Explanation:

Apply the FOIL method to expand the expression

$$ (2g + 3)(2g + 3) = (2g)(2g) + (2g)(3) + (3)(2g) + (3)(3) $$

Simplify individual terms

$$ (2g)(2g) = 4g^2 $$

$$ (2g)(3) + (3)(2g) = 6g + 6g = 12g $$

$$ (3)(3) = 9 $$

Combine like terms

$$ 4g^2 + 12g + 9 $$

Answer:

• (A) \(2g^2 + 12g - 9\)
• (B) \(4g^2 + 12g + 9\) (Correct answer)
• (C) \(2g^2 + 6g + 9\)
• (D) \(4g^2 + 6g + 9\)