Question

X to the power 4 plus four, factorise

Answer 1

Given :

x⁴ + 4

==> x⁴ + 4 + 4 x² - 4 x² [ add and subtract 4 x² ]

==> ( x² )² + 2² + 2.x².2 - 4 x²

==> ( x² + 2 )² - ( 2 x )² [ a² + b² + 2 ab = ( a + b )² ]

==> ( x² + 2 - 2 x )( x² + 2 + 2 x ) [ a² - b² = ( a + b )( a - b) ]

The answer is ( x² + 2 - 2 x )( x² + 2 + 2 x )

Hope it helps :-)

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