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Factorize (4a + 3)2 – (3a – 2)2

Factorize (4a + 3)2 – (3a – 2)2
  • A.
    (a + 1)(a + 5)
  • B.
    (a – 5)(7a – 1)
  • C.
    (a + 5)(7a + 1)
  • D.
    a(7a + 1)
Correct Answer: Option C
Explanation

(4a + 3)2 – (3a – 2)2 = a2 – b2
= (a + b)(a – b)
= [(4a + 3) + (3a – 2)][(4a + 3) + (3a – 2)]
= [(4a + 3 + 3a – 2)][(4a + 3 – 3a + 2)]
= (7a + 1)(a + 5)
∴ (a + 5)(7a + 1)