Question

Resolve x^18- y^18 into five factors.​

Answer 1

Answer:

Please see the attachment

Answer 2

Answer:

( x + y ) ( x - y ) ( x² + y² - xy ) ( x² + y² + xy ) ( x⁶ + y⁶ - x³y³ ) ( x⁶ + y⁶ + x³y³ )

Step-by-step explanation:

Given----> x¹⁸ - y¹⁸

To find ----> Factors of given expression

Solution-----> We know that,

1) a² - b² = ( a + b ) ( a - b )

2) a³ + b³ = ( a + b ) ( a² + b² - ab )

3) a³ - b³ = ( a - b ) ( a² + b² + ab )

Now,

x¹⁸ - y¹⁸ = ( x⁹ )² - ( y⁹ )²

Applying first identity , we get ,

= ( x⁹ + y⁹ ) ( x⁹ - y⁹ )

= { ( x³)³+( y³ )³ } { ( x³ )³ - ( y³ )³ }

Applying second and third identity , we get ,

= ( x³ + y³ ) { ( x³)² + ( y³ )² - x³y³ } ( x³ - y³ ) { ( x³ )² +

( y³ )² + x³ y³ }

Applying second and third identity again , we get

= ( x + y ) ( x² + y² - xy ) ( x⁶ + y⁶ - x³ y³ ) ( x - y ) ( x² + y² + xy ) ( x⁶ + y⁶ + x³y³ )

= ( x + y ) ( x - y ) ( x² + y² - xy ) ( x² + y² - xy ) ( x⁶ + y⁶ - x³y³ ) ( x⁶ + y⁶ + x⁶ y⁶ )