Question
Factorize: $x^2 - 1 - 2a - a^2$
✓
Answer
The given expression to be factorized is $x^2 - 1 - 2a - a^2$
Take common $-1$ from 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 $x^2 - 1 - 2a - a^2$
$= (x + 1 + a)(x - 1 - a).$
Take common $-1$ from 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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