Question

factorise x9-y9
Solve the problem please

Answer 1

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Answer 2

Answer:

$x^9-y^9=(x-y)(x^2+xy+y^2)(x^6+x^3y^3+y^6)$

Step-by-step explanation:

We have to factorize $x^9-y^9$

we use the following result:

x³ - y³ = (x - y)( x² + xy + y² )

Consider,

$x^9-y^9=(x^3)^3-(y^3)^3$

= ( x³ - y³ )( (x³)² + x³y³ + (y³)² )

$=(x^3-y^3)(x^6+x^3y^3+y^6)$

$=(x-y)(x^2+xy+y^2)(x^6+x^3y^3+y^6)$

Therefore, $x^9-y^9=(x-y)(x^2+xy+y^2)(x^6+x^3y^3+y^6)$