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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