Question

Find the factor of

a²_1-22 - x²​

Answer 1

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The required factor: (a - x - 1)(a + x + 1).

Step-by-step explanation:

$\tt{a² - 1 - 2x - x²} \\ \\ \tt{= a² - (1 + 2x + x²)} \\ \\ \sf{= a² - { (1)² + 2.1.x + (x)² } } \\ \\ \tt{= (a)² - (1 + x)² - - - - - - [∵ (x)² + 2.x.y + (y)² = (x + y)²]} \\ \\ \tt{= {a + (1 + x)} {a - (1 +x)} - - - - - - [∵ a² - b² = (a + b)(a - b)]} \\ \\ \\ \tt{= (a + x + 1)(a - x - 1) }$

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Answer 2

Answer:

*Refer the attachment.