`1/27 X^3 - Y^3 + 125z^3 + 5xy` - Mathematics

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Answer in Brief

`1/27 x^3 - y^3 + 125z^3 + 5xyz`

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Solution

`1/27 x^3 - y^3 + 125z^3 + 5xy`

`= (x/3)^3 + (-y)^3 + (5z)^3 - 3 xx x/3 (-y)(5z)`

`= (x/3 + (-y) + 5z)((x/3)^2 + (-y)^2 + (5z)^2 - x/3 (-y)- (-y)5z - 5z (x/3))`

`= (x/3 - y + 5z)(x^2/9 + y^2 + 25z^2 + (xy)/3 + 5xyz - 5/3 zx)`

`∴ 1/27 x^3 - y^3 + 125z^3 + 5xyz = (x/3 - y + 5z)(x^2/9 + y^2 + 25z^2 + (xy)/3 + 5yz - 5/3 zx)`

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Chapter 5: Factorisation of Algebraic Expressions - Exercise 5.4 [Page 23]

APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 5 Factorisation of Algebraic Expressions
Exercise 5.4 | Q 4 | Page 23

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