Question

factorise the following : x⁹ + y⁹​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

(x³+y³)³=(x³+y³)(x^6+2x³y³+y^6)=x^9+y^9+2x^6y³+x³y^6+x^6y³+2x³y^6=x^9+y^9+3x^6y³+3x³y^6=x^9+y^9+3x³y³(x³+y³).

Hence, x^9+y^9=(x³+y³)³-3x³y³(x³+y³).

Now take (x³+y³) as highest common factor.

(x³+y³)[(x³+y³)²-3x³y³]=x^9+y^9

And you could go on to factor the (x³+y³) parts which is equal to (x+y)(x²-2xy+y²)=(x+y)(x-y)²

x^9+y^9=(x+y)(x-y)²[(x+y)²(x-y)⁴-3x³y³]

Hope this helped.