Simplify (173 Xx 173 Xx 173 Xx 127 Xx 127 Xx 127)/(173 Xx 173 Xx 173 Xx 127 Xx 127 Xx 127) - Mathematics

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Simplify `(173 xx 173 xx 173 xx 127 xx 127 xx 127)/(173 xx 173 xx 173 xx 127 xx 127 xx 127)`

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Solution

 `(173 xx 173 xx 173 xx 127 xx 127 xx 127)/(173 xx 173 xx 173 xx 127 xx 127 xx 127)`

`= (173^2 + 127^3)/(173^2 - 173 xx 127 + 127^2)`

`= ((173 + 127)(173^3 - 173 xx 127 + 127^2))/(173^2 - 173 xx 127 + 127^2)`        `[∵ a^3 - b^3 = (a - b)(a^2 + ab + b^2)]` 

`= (a - 1/a)(a^2 + 1 + 1/a^2) - 2(a - 1/a)`

`= (a - 1/a)(a^2 + 1 + 1/a^2 - 2)`

`= (a - 1/a)(a^2 + 1/a^2 - 1)`

`∴ a^3 - 1/a^3 - 2a + 2/a = (a - 1/a)(a^2 + 1/a^2 - 1)`

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Chapter 5: Factorisation of Algebraic Expressions - Exercise 5.2 [Page 14]

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RD Sharma Mathematics for Class 9
Chapter 5 Factorisation of Algebraic Expressions
Exercise 5.2 | Q 16.1 | Page 14

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