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# Ex.2.5 Q13 Polynomials Solution - NCERT Maths Class 9

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## Question

If  \begin{align}x+y+z=0,\end{align}

show that  \begin{align}x^{3}+y^{3}+z^{3}=3 x y z\end{align}

Video Solution
Polynomials
Ex 2.5 | Question 13

## Text Solution

Reasoning:

Identity:

\begin{align}&x^{3}+y^{3}+z^{3}-3 x y z\\&=\!(x\!+\!y\!+\!z)\left(x^{2}\!+\!y^{2}\!+\!z^{2}\!-\!x y\!-\!y z\!-\!zx\right)\end{align}

Steps:

By the identity:

\begin{align}&x^{3}+y^{3}+z^{3}-3 x y z\\&=\!(x\!+\!y\!+\!z)\left(x^{2}\!+\!y^{2}\!+\!z^{2}\!-\!x y\!-\!y z\!-\!zx\right)\end{align}

If  $$x + y + z = 0$$  then the entire $$RHS$$ becomes $$0$$ and hence the $$LHS$$

\begin{align}x^{3}+y^{3}+z^{3}-3 x y z=0\end{align}

Hence,

\begin{align}x^{3}+y^{3}+z^{3}=3 x y z\end{align}

Video Solution
Polynomials
Ex 2.5 | Question 13

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