Factorize 8/27 X^3 + 1 + 4/3 X^2 + 2x - Mathematics

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Factorize `8/27 x^3 + 1 + 4/3 x^2 + 2x`

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Solution

`= (2/3 x)^3 + (1)^3 + 3 xx (2/3 x)^2 xx 1 + 3(1)^2 xx (2/3 x)`

`= (2/3 x  + 1)^3          [∵ a^3 + b^3 + 3a^2b + 3ab^2 = (a + b)^2]`

`= (2/3 x + 1)(2/3x + 1)(2/3x + 1)`

`∴ 8/27 x^3 + 1 + 4/3 x^2 + 2x = (2/3x + 1)(2/3 x + 1)(2/3x + 1)`

 

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Chapter 5: Factorisation of Algebraic Expressions - Exercise 5.3 [Page 17]

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RD Sharma Mathematics for Class 9
Chapter 5 Factorisation of Algebraic Expressions
Exercise 5.3 | Q 3 | Page 17

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