To simplify the expression \((2x-9)(x+6)\), you can use the distributive property, also known as the FOIL method for binomials. The FOIL method stands for First, Outer, Inner, Last, which represents the terms you need to multiply together:
1. First: Multiply the first terms in each binomial.
2. Outer: Multiply the outer terms.
3. Inner: Multiply the inner terms.
4. Last: Multiply the last terms in each binomial.
Let's apply these steps to our given expression:
[tex]\[
(2x - 9)(x + 6)
\][/tex]
1. First: Multiply the first terms:
[tex]\[
2x \cdot x = 2x^2
\][/tex]
2. Outer: Multiply the outer terms:
[tex]\[
2x \cdot 6 = 12x
\][/tex]
3. Inner: Multiply the inner terms:
[tex]\[
-9 \cdot x = -9x
\][/tex]
4. Last: Multiply the last terms:
[tex]\[
-9 \cdot 6 = -54
\][/tex]
Now, add all the results together:
[tex]\[
2x^2 + 12x - 9x - 54
\][/tex]
Combine the like terms \(12x\) and \(-9x\):
[tex]\[
2x^2 + 3x - 54
\][/tex]
Therefore, the simplified expression is:
[tex]\[
2x^2 + 3x - 54
\][/tex]
So the correct answer is:
C. [tex]\(2x^2 + 3x - 54\)[/tex]
