Factorize Xy9 - Yx9 - Mathematics

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Factorize xy9 - yx9

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Solution

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 )

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Chapter 5: Factorisation of Algebraic Expressions - Exercise 5.1 [Page 9]

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RD Sharma Mathematics for Class 9
Chapter 5 Factorisation of Algebraic Expressions
Exercise 5.1 | Q 24 | Page 9

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