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
Write the coefficient of $x^{2}$ in the following polynomial: $\sqrt{3} x^{2}+11$.
Easy
View SolutionIf $a, b, c$ are all non-zero and $a+b+c=0,$ prove that $\frac{a^{2}}{b c}+\frac{b^{2}}{c a}+\frac{c^{2}}{a b}=3$.
Easy
View SolutionWithout actually calculating the cubes,find the value of each of the following:
$(31)^{3} - (16)^{3} - (15)^{3}$
$(31)^{3} - (16)^{3} - (15)^{3}$
Difficult
View SolutionEvaluate $(65)^{2}$.
Easy
View SolutionState whether the following statement is true or false:
$x^{2}-5x+4$ is a linear polynomial.
$x^{2}-5x+4$ is a linear polynomial.
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