Question

expand and simplify \\((3x + 2)(x + 9)\\)

Explanation:

Apply the distributive property to expand the binomials

$$ (3x + 2)(x + 9) = 3x(x + 9) + 2(x + 9) $$

Distribute terms individually

$$ 3x(x) + 3x(9) + 2(x) + 2(9) = 3x^2 + 27x + 2x + 18 $$

Combine like terms

$$ 3x^2 + (27x + 2x) + 18 = 3x^2 + 29x + 18 $$

Answer:

\(3x^2 + 29x + 18\)