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)
jamb 1992mathematics

The correct answer is C. (3p - q + 3r)(3p + q - 3r)

\(9p^{2} - q^{2} + 6qr - 9r^{2}\)

= \(9p^{2} - (q^{2} - 6qr + 9r^{2})\)

= \(9p^{2} - (q^{2} - 3qr - 3qr + 9r^{2})\)

= \(9p^{2} - (q(q - 3r) - 3r(q - 3r))\)

= \(9p^{2} - (q - 3r)^{2}\)

= \((3p + (q - 3r))(3p - (q - 3r))\)

= \((3p + q - 3r)(3p - q + 3r)\)

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