Question

what is the product of the polynomials below?
(9x + 9)(x + 2)
a. $9x^2 + 11x + 18$
b. $9x^2 + 27x + 162$
c. $9x^2 + 11x + 9$
d. $9x^2 + 27x + 18$

Explanation:

Step1: Apply distributive property (FOIL)

Multiply each term in the first polynomial by each term in the second polynomial:
$(9x + 9)(x + 2) = 9x \cdot x + 9x \cdot 2 + 9 \cdot x + 9 \cdot 2$

Step2: Simplify each term

Calculate each product:
$9x \cdot x = 9x^2$,
$9x \cdot 2 = 18x$,
$9 \cdot x = 9x$,
$9 \cdot 2 = 18$

Step3: Combine like terms

Add the $x$-terms: $18x + 9x = 27x$.
Combine all terms: $9x^2 + 27x + 18$

Answer:

D. $9x^2 + 27x + 18$