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Question
Factorize : x2 − 1 − 2a − a2
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Solution
The given expression to be factorized is
`x^2 -1 -2a -a^2`
Take common -1from the last three terms and then we have
`x^2 - 1 -2a - a^2`
` = x^2 - (1+2a + a^2)`
` = x^2 - {(1)^2 + 2.1.a+ (a)^2}`
` = x^2 - (1+ a)^2`
` = (x)^2 - (1+a)^2`
` = {x+ (1+ a)}{x-(1+a)}`
` = (x+1+a)(x-1-a)`
We cannot further factorize the expression.
So, the required factorization is `x^2 -1 -2a - a^2 = (x+1 + a)(x-1-a)`.
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