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प्रश्न
Factorize xy9 - yx9
उत्तर
xy9 - yx9
= xy ( y8 - x8 )
= xy (( y4)2 - (x4 )2 )
Using identity a2 - b2 = (a + b)(a - b)
= xy ( y4 + x4 )( y4 - x4 )
= xy ( y4 + x4 )(( y2)2 - (x2 )2 )
Using identity a2 - b2 = (a + b)(a - b)
= xy ( y4 + x4 )( y2 + x2 )( y2 - x2 )
= xy ( y4 + x4 )( y2 + x2 )( y + x)( y - x)
= xy (x4 + y4 )(x2 + y2 )( x + y )(-1)( x - y )
∵ (b - a) = -1(a - b)
= -xy (x4 + y4 )(x2 + y2 )( x + y )( x - y )
∴ xy9 - yx9 = -xy (x4 + y4 )(x2 + y2 )(x + y )(x - y )
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