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)
Correct Answer: Option C
Explanation
(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))