Which expression is equivelent to (2x + 9) (x - 2)?

1 answer

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:

  1. \(2x \cdot x = 2x^2\)
  2. \(2x \cdot (-2) = -4x\)
  3. \(9 \cdot x = 9x\)
  4. \(9 \cdot (-2) = -18\)

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:

\[ \boxed{2x^2 + 5x - 18} \]