pls make it fast:- factorize x^9+y^9
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Step-by-step explanation:
We have to factorize x^9-y^9x
9
−y
9
we use the following result:
x³ - y³ = (x - y)( x² + xy + y² )
Consider,
x^9-y^9=(x^3)^3-(y^3)^3x
9
−y
9
=(x
3
)
3
−(y
3
)
3
= ( x³ - y³ )( (x³)² + x³y³ + (y³)² )
=(x^3-y^3)(x^6+x^3y^3+y^6)=(x
3
−y
3
)(x
6
+x
3
y
3
+y
6
)
=(x-y)(x^2+xy+y^2)(x^6+x^3y^3+y^6)=(x−y)(x
2
+xy+y
2
)(x
6
+x
3
y
3
+y
6
)
Therefore, x^9-y^9=(x-y)(x^2+xy+y^2)(x^6+x^3y^3+y^6)x
9
−y
9
=(x−y)(x
2
+xy+y
2
)(x
6
+x
3
y
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