Factorize \(9p^2 - q^2 + 6qr - 9r^2\)
A
(3p - 3q + r)(3p - q - 3r)
B
(6p - 3q - 3r)(3p - q - 4r)
C
(3p - q + 3r)(3p + q - 3r)
D
(3q - p + 3r)(3q - p + 3r)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(9p^{2} - q^{2} + 6qr - 9r^{2}\)
= \(9p^{2} - (q^{2} - 6qr + 9r^{2})\)
= \(9p^{2} - (q^{2} - 3qr - 3qr + 9r^{2})\)
= \(9p^{2} - (q(q - 3r) - 3r(q - 3r))\)
= \(9p^{2} - (q - 3r)^{2}\)
= \((3p + (q - 3r))(3p - (q - 3r))\)
= \((3p + q - 3r)(3p - q + 3r)\)
Source: Myschool Past Questions Archive (Record #31307)