x12 = 120 , y12 = 260, sx= 24 , sy= 12 , r = -0.8 ,x= 4,00,000, b= ?
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\begin{gathered} = {x}^{12} - {y}^{12} \\ = {( {x}^{6} )}^{2} - {( {y}^{6} )}^{2} \\ = ( {x}^{6} + {y}^{6} )( {x}^{6} - {y}^{6} ) \\ = ( {x}^{6} + {y}^{6} )( {( {x}^{3} )}^{2} - {( {y}^{3} )}^{2} ) \\ = ( {x}^{6} + {y}^{6} )( {x}^{3} + {y}^{3} )( {x}^{3} - {y}^{3} ) \\ = ( {x}^{6} + {y}^{6} )(x + y)( {x}^{2} - xy + {y}^{2} )(x - y)( {x}^{2} + xy + {y}^{2} )\end{gathered}
=x
12
−y
12
=(x
6
)
2
−(y
6
)
2
=(x
6
+y
6
)(x
6
−y
6
)
=(x
6
+y
6
)((x
3
)
2
−(y
3
)
2
)
=(x
6
+y
6
)(x
3
+y
3
)(x
3
−y
3
)
=(x
6
+y
6
)(x+y)(x
2
−xy+y
2
)(x−y)(x
2
+xy+y
2
)
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