Factorise: $a^{12} - b^{12}$

(a^{6} + b^{6}) (a + b) (a^{2} - a b - b^{2}) (a^{2} + a b + b^{2})

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(a^{2} + b^{2}) (a^{4} + b^{4} - a^{2} b^{2}) (a + b) (a^{2} + b^{2} - a b) (a - b) (a^{2} + b^{2} + a b)

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(a^{6} + b^{6}) (a - b) (a^{2} - a b + b^{2}) (a^{2} + a b + b^{2})

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(a^{6} - b^{6}) (a + b) (a^{2} - a b + b^{2}) (a^{2} + a b + b^{2})

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Solution

The correct option is C $(a^{2} + b^{2}) (a^{4} + b^{4} - a^{2} b^{2}) (a + b) (a^{2} + b^{2} - a b) (a - b) (a^{2} + b^{2} + a b)$
$a^{12} - b^{12}$
$= {(a^{6})}^{2} - {(b^{6})}^{2}$
$= (a^{6} - b^{6}) (a^{6} + b^{6})$
$= [{(a^{2})}^{3} + {(b^{2})}^{3}] [{(a^{3})}^{2} - {(b^{3})}^{2}]$
$= (a^{2} + b^{2}) (a^{4} + b^{4} - a^{2} b^{2}) (a^{3} + b^{3}) (a^{3} - b^{3})$
$= (a^{2} + b^{2}) (a^{4} + b^{4} - a^{2} b^{2}) (a + b) (a^{2} + b^{2} - a b) (a - b) (a^{2} + b^{2} + a b)$

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a^{6} - b^{6}

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

Question 84 (ix)

Simplify

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

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