Factorize :
$a - b - a^{3} + b^{3}$

(2 a - b) (1 - a^{2} + a b - b^{2})

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(a - b) (1 - a^{2} - a - b^{2})

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(a + b) (1 - a^{2} - a - b^{2})

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(2 a - b) (1 - a^{2} - a b - b^{2})

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Solution

The correct option is A $(2 a - b) (1 - a^{2} + a b - b^{2})$
$a - b - a^{3} + b^{3}$
$= (a - b) - (a^{3} - b^{3})$
$= (a - b) - (a - b) (a^{2} + a b + b^{2})$
$= (a - b) (1 - (a^{2} + a b + b^{2}))$
$= (a - b) (1 - a^{2} - a b - b^{2})$

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Factorize :a−b−a3+b3

The correct option is A (2a−b)(1−a2+ab−b2) a−b−a3+b3=(a−b)−(a3−b3)=(a−b)−(a−b)(a2+ab+b2)=(a−b)(1−(a2+ab+b2))=(a−b)(1−a2−ab−b2)

Factorize :
$a - b - a^{3} + b^{3}$

The correct option is A $(2 a - b) (1 - a^{2} + a b - b^{2})$
$a - b - a^{3} + b^{3}$
$= (a - b) - (a^{3} - b^{3})$
$= (a - b) - (a - b) (a^{2} + a b + b^{2})$
$= (a - b) (1 - (a^{2} + a b + b^{2}))$
$= (a - b) (1 - a^{2} - a b - b^{2})$