Question
Which expression is equivelent to (2x + 9) (x - 2)?
Answers
GPT-4o mini
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:
\[
\boxed{2x^2 + 5x - 18}
\]
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:
\[
\boxed{2x^2 + 5x - 18}
\]