\(\rm \frac{(a-b+c)^2-(a-b-c)^2}{b-a}\) সমান

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CTET (Mathematics & Science) Official Paper-II (Held On: 07 Jul, 2024)
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  1. -4c
  2. 2c
  3. b - a
  4. c - a

Answer (Detailed Solution Below)

Option 1 : -4c
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ধারণা -

a2 - b2 = (a - b)(a + b)

ব্যাখ্যা -

আমাদের আছে \(\rm \frac{(a-b+c)^2-(a-b-c)^2}{b-a}\)

= \(\rm \frac{(a-b+c-(a-b-c))(a-b+c+(a-b-c))}{b-a}\)

= \(\rm \frac{(a-b+c-a+b+c)(a-b+c+a-b-c)}{b-a}\)

= \(\rm \frac{(c+c)(a-b+a-b)}{b-a}\)

= \(\rm \frac{(2c)(2a-2b)}{b-a} = \rm \frac{(2c)\times -2(b-a)}{b-a} = -4c\)

অতএব বিকল্প (1) সঠিক।

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