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Mathematics

Assertion(A): One of the factors of (5x + 1)2 + (25x2 - 1) is 2x.

Reason(R): (a + b)2 = (a + b)(a + b) and a2 - b2 = (a + b)(a - b)

  1. A is true, R is false

  2. A is false, R is true

  3. Both A and R are true

  4. Both A and R are false

Factorisation

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Answer

Given,

⇒ (5x + 1)2 + (25x2 - 1)

⇒ (5x + 1)2 + (5x)2 - (1)2

⇒ (5x + 1)2 + (5x + 1)(5x - 1)

⇒ (5x + 1)[(5x + 1) + (5x - 1)]

⇒ (5x + 1)(10x)

⇒ 2x(5)(5x + 1).

Assertion (A) is true.

⇒ (a + b)2 can be written as (a + b)(a + b)

By identity,

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

Reason (R) is true.

Thus, both A and R are true.

Hence, option 3 is correct option.

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