To simplify the expression [tex]\((2x - 9)(x + 6)\)[/tex], we need to use the distributive property (also known as the FOIL method for binomials). Let's break it down step by step:
1. First, multiply the first terms in each binomial:
[tex]\[
2x \cdot x = 2x^2
\][/tex]
2. Outside, multiply the outer terms in the binomials:
[tex]\[
2x \cdot 6 = 12x
\][/tex]
3. Inside, multiply the inner terms in the binomials:
[tex]\[
-9 \cdot x = -9x
\][/tex]
4. Last, multiply the last terms in each binomial:
[tex]\[
-9 \cdot 6 = -54
\][/tex]
Now, add all these results together:
[tex]\[
2x^2 + 12x - 9x - 54
\][/tex]
Combine the like terms:
[tex]\[
2x^2 + (12x - 9x) - 54 = 2x^2 + 3x - 54
\][/tex]
Therefore, the simplified expression is:
[tex]\[
2x^2 + 3x - 54
\][/tex]
So, the correct answer is:
C. [tex]\(2x^2 + 3x - 54\)[/tex]
