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NECO 2023 · Paper 1 · Q30

Factorize 12a2−3(a−3b)212a^2 - 3(a - 3b)^2 completely.

Worked solution (try it first)
  1. Take out the common factor 3: 3[4a2−(a−3b)2]=3[(2a)2−(a−3b)2]3[4a^2 - (a - 3b)^2] = 3[(2a)^2 - (a - 3b)^2].
  2. Difference of two squares: (2a−a+3b)(2a+a−3b)=(a+3b)(3a−3b)(2a - a + 3b)(2a + a - 3b) = (a + 3b)(3a - 3b).
  3. Take out 3 from 3a−3b3a - 3b: 3×3(a+3b)(a−b)=9(a+3b)(a−b)3 \times 3(a + 3b)(a - b) = 9(a + 3b)(a - b), option A.

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