12. Find the LCM x3+y3, x3-y3, x4+x2y2+y4
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Given, x
3
+y
3
,x
3
−y
3
,x
4
+x
2
y
2
+y
4
⇒x
3
+y
3
=(x+y)(x
2
−xy+x
2
)
⇒x
3
−y
3
=(x−y)(x
2
+xy+y
2
)
⇒x
4
+x
2
y
2
+y
4
=(x
2
+y
2
)
2
−x
2
y
2
=(x
2
+y
2
)
2
−(xy)
2
=(x
2
+y
2
+xy)(x
2
+y
2
−xy)
L.C.M. =(x+y)(x
2
−xy+y
2
)
(x−y)(x
2
+xy+y
2
)
=(x
3
+y
3
)(x
3
−y
3
)
=(x
3
)
2
−y
3
)
2
−x
6
−y
6
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