Question

Factorize xy⁹ - yx⁹

Answer 1

xy⁹ - yx⁹

= xy ( y⁸  - x⁸ )

= xy (( y⁴)²  - (x⁴ )² )

Using identity a² - b² = (a + b)(a - b)

= xy ( y⁴  + x⁴ )( y⁴  - x⁴ )

= xy ( y⁴  + x⁴ )(( y²)²  - (x² )² )

Using identity a² - b² = (a + b)(a - b)

= xy ( y⁴  + x⁴ )( y²  + x² )( y²  - x² )

= xy ( y⁴  + x⁴ )( y²  + x² )( y + x)( y - x)

= xy (x⁴ + y⁴ )(x² + y² )( x + y )(-1)( x - y )

∵ (b - a) = -1(a - b)

= -xy (x⁴  + y⁴ )(x²  + y² )( x + y )( x - y )

∴ xy⁹ - yx⁹  = -xy (x⁴ + y⁴ )(x² + y² )(x + y )(x - y )