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)
jamb 1986mathematics

The correct answer is C. (a + 5)(7a + 1)

\((4a + 3)^2- (3a - 2)^2\)

=\((4a + 3) + (3a - 2)\) * \((4a + 3) - (3a - 2)\)

= \((4a + 3 + 3a - 2)\) * \((4a + 3 - 3a + 2)\)

= \((7a + 1)\) * \((a + 5)\)

= (a + 5)(7a + 1)

Hence, the expression \((4a + 3)^2- (3a - 2)^2\) can be factorized completely as (a + 5)(7a + 1).

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