Factorize : $a^{6} - b^{6}$

(b - a) (a + b) (a^{3} + a b + b^{3}) (a^{2} - a b + b^{2})

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

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

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(a + b) (a - b) (a^{2} + a b + b^{2}) (a^{3} - a b + b^{3})

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Solution

The correct option is B $(a - b) (a + b) (a^{2} + a b + b^{2}) (a^{2} - a b + b^{2})$
$a^{6} - b^{6}$
$= (a^{2})^{3} - (b^{2})^{3}$
Using,
$(a^{3} - b^{3}) = (a - b) (a^{2} + a b + b^{2})$
$= (a^{2} - b^{2}) [(a^{2})^{2} + a^{2} b^{2} + (b^{2})^{2}]$
$= (a + b) (a - b) [(a^{2})^{2} + 2 a^{2} b^{2} + (b^{2})^{2} - a^{2} b^{2}]$
$= (a + b) (a - b) [(a^{2} + b^{2})^{2} - a^{2} b^{2}]$
$= (a + b) (a - b) [(a^{2} + b^{2} + a b) (a^{2} + b^{2} - a b)]$

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Similar questions

On Resolving $a^{6} - b^{6}$ into factors give $(a + b) (a - b) (a^{2} - a b + b^{2}) (a^{2} + a b + b^{2})$ .

$The product (a + b) (a - b) (a^{2} - a b + b^{2}) (a^{2} + a b + b^{2})$ is equal to

a^{6} - b^{6}

Question 84 (ix)

Simplify

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

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