Question

simplify the expression (2x - 9)(x + 6).

a. 2x² - 54
b. 2x² - 3x - 54
c. 2x² + 3x - 54
d. 2x² + 21x - 54

Explanation:

Step1: Apply the distributive property (FOIL method)

Multiply each term in the first binomial by each term in the second binomial:
\((2x - 9)(x + 6)=2x\cdot x+2x\cdot6 - 9\cdot x - 9\cdot6\)

Step2: Simplify each product

Simplify each term:
\(2x\cdot x = 2x^{2}\), \(2x\cdot6 = 12x\), \(-9\cdot x=-9x\), \(-9\cdot6 = - 54\)
So the expression becomes \(2x^{2}+12x - 9x-54\)

Step3: Combine like terms

Combine the \(x\) terms: \(12x-9x = 3x\)
The simplified expression is \(2x^{2}+3x - 54\)

Answer:

C. \(2x^{2}+3x - 54\)