Without finding the cubes,factorise $(x-2 y)^{3}+(2 y-3 z)^{3}+(3 z-x)^{3}$.
(D) Let $a = x-2y$,$b = 2y-3z$,and $c = 3z-x$.
Then,$a+b+c = (x-2y) + (2y-3z) + (3z-x) = 0$.
We know that if $a+b+c = 0$,then $a^3 + b^3 + c^3 = 3abc$.
Substituting the values of $a, b,$ and $c$ back into the identity,we get:
$(x-2y)^3 + (2y-3z)^3 + (3z-x)^3 = 3(x-2y)(2y-3z)(3z-x)$.
Then,$a+b+c = (x-2y) + (2y-3z) + (3z-x) = 0$.
We know that if $a+b+c = 0$,then $a^3 + b^3 + c^3 = 3abc$.
Substituting the values of $a, b,$ and $c$ back into the identity,we get:
$(x-2y)^3 + (2y-3z)^3 + (3z-x)^3 = 3(x-2y)(2y-3z)(3z-x)$.
Explore More
Similar Questions
Check whether $p(x)$ is a multiple of $g(x)$ or not:
$p(x) = x^{3} - 5x^{2} + 4x - 3, \quad g(x) = x - 2$
$p(x) = x^{3} - 5x^{2} + 4x - 3, \quad g(x) = x - 2$
Easy
View SolutionIf $x+y=12$ and $xy=27$,find the value of $x^{3}+y^{3}$.
Medium
View SolutionClassify the following as linear,quadratic,or cubic polynomial:
$5t + 3$
$5t + 3$
Easy
View SolutionFactorise the following:
$1-64 a^{3}-12 a+48 a^{2}$
$1-64 a^{3}-12 a+48 a^{2}$
Easy
View SolutionIf $x+1$ is a factor of $ax^3+x^2-2x+4a-9$,find the value of $a$.
Easy
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo