Question

factorise x^16 -y^16

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Answer 1

Here's your answer in this pic.

Answer 2

$x^{16} - y^{16} \\= (x^{8})^{2} - (y^{8})^{2} \\= ( x^{8} + y^{8} )( x^{8} - y^{8} )$

$\boxed {\pink { Since, a^{2} - b^{2} = ( a + b )( a - b ) }}$

$= ( x^{8} + y^{8} )[ (x^{4})^{2} - (y^{4})^{2} ]$

$= ( x^{8} + y^{8} ) (x^{4} + y^{4}) ( x^{4} - y^{4} )$

$= ( x^{8} + y^{8} ) (x^{4} + y^{4}) [ (x^{2})^{2} - (y^{2} )^{2}]$

$= ( x^{8} + y^{8} ) (x^{4} + y^{4}) (x^{2} + y^{2} )( x^{2} - y^{2} )$

$= ( x^{8} + y^{8} ) (x^{4} + y^{4}) (x^{2} + y^{2} )(x + y )( x- y)$

Therefore.,

$\red { Factors \: of \: x^{16} - y^{16}}\\\green {= ( x^{8} + y^{8} ) (x^{4}+ y^{4}) (x^{2} + y^{2} )(x + y )( x- y)}$

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