27x3 − Y3 − Z3 − 9xyz - Mathematics

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Answer in Brief

27x3 − y3 − z3 − 9xyz

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Solution

 

The given expression to be factorized is

 `27x^3 - y ^3 z^3 - 9xyz`

This can be written in the form

`27x^3 - y^3 - z^3 - 9xyz = (3x)^3 + (-y)^3+(-z)^3 -3 (3x)(-y)(-z)`

Recall the formula

`a^3+b^3 +c^3 -3abc = (a+b+c)(a^2 +b^2 +c^2 - ab - bc -ca)`

Using the above formula, we have

`27x^3 - y^3 -z^3 - 9xyz`

`={3x +(-y) + (-z)}{(3x)^2 + (-y)^2+ (-z)^2 - (3x)(-y)-(-y)(-z )- (-z)(3x)}`

` = (3x-y -z)(9x^2 +y^2 +z^2 + 3xy - yz + 3zx)`

We cannot further factorize the expression. 

So, the required factorization is of  `27x^3 - y^3-z^3 -9xyz` is  `(3x -y-z)(9x^2 +y^2 +z^2 +3xy -yz +3zx)`.

  Is there an error in this question or solution?
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 3 | Page 23

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