Question

what is ((7r + 2)(3r^2 + 5r - 3))?
a. (21r^3 + 41r^2 - 11r - 6)
b. (21r^3 + 41r^2 - 10r - 6)
c. (20r^3 + 41r^2 - 11r - 5)
d. (21r^3 + 42r^2 - 10r - 6)

Explanation:

Step1: Distribute $7r$ to each term

$7r \times 3r^2 + 7r \times 5r + 7r \times (-3) = 21r^3 + 35r^2 - 21r$

Step2: Distribute $2$ to each term

$2 \times 3r^2 + 2 \times 5r + 2 \times (-3) = 6r^2 + 10r - 6$

Step3: Combine like terms

$21r^3 + (35r^2+6r^2) + (-21r+10r) -6 = 21r^3 + 41r^2 -10r -6$

Answer:

b. $21r^{3}+41r^{2}-10r-6$