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JAMB 1992 · UME · Q11

Factorize 9p2−q2+6qr−9r29p^2 - q^2 + 6qr - 9r^2.

Worked solution (try it first)
  1. Group the last three terms: 9p2−(q2−6qr+9r2)9p^2 - (q^2 - 6qr + 9r^2).
  2. The bracket is a perfect square, (q−3r)2(q - 3r)^2, so the expression is (3p)2−(q−3r)2(3p)^2 - (q - 3r)^2.
  3. Difference of two squares: [3p−(q−3r)][3p+(q−3r)][3p - (q - 3r)][3p + (q - 3r)], which is (3p−q+3r)(3p+q−3r)(3p - q + 3r)(3p + q - 3r), option C.

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