To find an expression equivalent to \((2x + 9)(x - 2)\), we can use the distributive property (also known as the FOIL method for binomials).
Let's distribute each term in the first binomial to each term in the second binomial:
\[ (2x + 9)(x - 2) = 2x \cdot x + 2x \cdot (-2) + 9 \cdot x + 9 \cdot (-2) \]
Calculating each term:
- \(2x \cdot x = 2x^2\)
- \(2x \cdot (-2) = -4x\)
- \(9 \cdot x = 9x\)
- \(9 \cdot (-2) = -18\)
Now, combine all the results:
\[ 2x^2 - 4x + 9x - 18 \]
Next, combine the like terms \(-4x\) and \(9x\):
\[ 2x^2 + 5x - 18 \]
Therefore, the expression equivalent to \((2x + 9)(x - 2)\) is:
\[ \boxed{2x^2 + 5x - 18} \]