Factorise the following expression: $8x^3 + 343y^3 + 84x^2y + 294xy^2$.
(N/A) The given expression is $8x^3 + 343y^3 + 84x^2y + 294xy^2$.
We can rewrite this as $(2x)^3 + (7y)^3 + 3(2x)^2(7y) + 3(2x)(7y)^2$.
This expression is in the form of the algebraic identity $a^3 + b^3 + 3a^2b + 3ab^2 = (a + b)^3$,where $a = 2x$ and $b = 7y$.
Substituting these values,we get $(2x + 7y)^3$.
Thus,the factorised form is $(2x + 7y)(2x + 7y)(2x + 7y)$.
We can rewrite this as $(2x)^3 + (7y)^3 + 3(2x)^2(7y) + 3(2x)(7y)^2$.
This expression is in the form of the algebraic identity $a^3 + b^3 + 3a^2b + 3ab^2 = (a + b)^3$,where $a = 2x$ and $b = 7y$.
Substituting these values,we get $(2x + 7y)^3$.
Thus,the factorised form is $(2x + 7y)(2x + 7y)(2x + 7y)$.
Explore More
Similar Questions
Classify the following polynomial as a polynomial in one variable,two variables,etc.:
$x y + y z + z x$
$x y + y z + z x$
Easy
View SolutionIf $x-2$ is a factor of $x^{3}-3x^{2}+ax+24$,then $a = \ldots$
Easy
View SolutionShow that $2x - 3$ is a factor of $x + 2x^3 - 9x^2 + 12$.
Medium
View SolutionFactorise:
$2 \sqrt{2} a^{3} + 8 b^{3} - 27 c^{3} + 18 \sqrt{2} a b c$
$2 \sqrt{2} a^{3} + 8 b^{3} - 27 c^{3} + 18 \sqrt{2} a b c$
Medium
View SolutionFind the following product:
$\left(\frac{x}{2}+2 y\right)\left(\frac{x^{2}}{4}-x y+4 y^{2}\right)$
$\left(\frac{x}{2}+2 y\right)\left(\frac{x^{2}}{4}-x y+4 y^{2}\right)$
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