(x-y)÷(x⁶+y⁶) by long division method find the answer
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Answer:
We know the identity a
3
−b
3
=(a−b)(a
2
+b
2
+ab)
Using the above identity, the equation x
6
−y
6
can be factorised as follows:
x
6
−y
6
=(x
2
)
3
−(y
2
)
3
=(x
2
−y
2
)[(x
2
)
2
+(y
2
)
2
+(x
2
×y
2
)]=(x−y)(x+y)(x
2
+y
2
+xy)(x
2
+y
2
−xy)
(using identities a
2
−b
2
=(a+b)(a−b) and a
4
+b
4
+a
2
b
2
=(a
2
+b
2
+ab)(a
2
+b
2
−ab) )
Hence, x
6
−y
6
=(x−y)(x+y)(x
2
+y
2
+xy)(x
2
+y
2
−xy)
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