X3 - 8y3 + 27z3 +18xyz - Mathematics

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x3 - 8y3 + 27z3 +18xyz

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Solution

= x3  + (-2 y )3  + (3z )3  - 3 × x × (-2 y )(3z )

= (x + (-2 y ) + 3z )(x2   + (-2y)2   + (3z)2   - x (-2y) - (-2y)(3z) - 3z (x ))        [∵  a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca )]

= ( x - 2 y + 3z )(x2 + 4 y2 + 9z2 + 2xy + 6 yz - 3zx)

∴ x3  - 8y3  + 27z3  +18xyz = ( x - 2 y + 3z )(x2  + 4 y2  + 9z2  + 2xy + 6 yz - 3zx)

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

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RD Sharma Mathematics for Class 9
Chapter 5 Factorisation of Algebraic Expressions
Exercise 5.4 | Q 2 | Page 23

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