Question
The factors of $a^2 - 1 - 2x - x^2,$ are.
✓
Answer
The given expression to be factorized is $a^2 - 1 - 2x - x^2$
Take common $-1$ from the last three terms and then we have
$a^2 - 1 - 2x - x^2 = a^2 - (1 + 2x + x^3)$
$= a^2 - {(1)^2 + 2.1 \times x + (x)^2}$
$= a^2 - (1 + x)^2$
$= (a)^2- (1 + x)^2$
$= {a + (1 + x)} {a - (1 + x)}$
$= (a + 1 + x) (a - 1 - x)$
$= (a + x + 1) (a - x - 1)$
Take common $-1$ from the last three terms and then we have
$a^2 - 1 - 2x - x^2 = a^2 - (1 + 2x + x^3)$
$= a^2 - {(1)^2 + 2.1 \times x + (x)^2}$
$= a^2 - (1 + x)^2$
$= (a)^2- (1 + x)^2$
$= {a + (1 + x)} {a - (1 + x)}$
$= (a + 1 + x) (a - 1 - x)$
$= (a + x + 1) (a - x - 1)$
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