Question : If $xy(x+y)=m$, then the value of $(x^3+y^3+3m)$ is:
Option 1: $\frac{m^3}{xy}$
Option 2: $\frac{m^3}{(x+y)^3}$
Option 3: $\frac{m^3}{x^3y^3}$
Option 4: $mx^3y^3$
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Correct Answer: $\frac{m^3}{x^3y^3}$
Solution :
Given: $xy(x+y)=m$
We know that the algebraic identity is $(x+y)^3=x^3+y^3+3xy(x+y)$.
$xy(x+y)=m$
⇒ $(x+y)=\frac{m}{xy}$
Take the cube on both sides of the above equation, we get,
$(x+y)^3=(\frac{m}{xy})^3$
⇒ $x^3+y^3+3xy(x+y)=\frac{m^3}{x^3y^3}$
Substitute the value of $xy(x+y)=m$ in above equation, we get,
$x^3+y^3+3m=\frac{m^3}{x^3y^3}$
Hence, the correct answer is $\frac{m^3}{x^3y^3}$.
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