Check whether the following is a quadratic equation: $(x + 2)^{3} = 2 x (x^{2} - 1)$

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Solution

Given: $(x + 2)^{3} = 2 x (x^{2} - 1)$
$\Rightarrow x^{3} + 8 + 6 x^{2} + 12 x = 2 x^{3} - 2 x$ [Using $(a + b)^{3} = a^{3} + b^{3} + 3 a^{2} b + 3 a b^{2}$ ]
$\Rightarrow x^{3} - 2 x^{3} + 6 x^{2} + 12 x + 2 x + 8 = 0$
$\Rightarrow - x^{3} + 6 x^{2} + 14 x + 8 = 0$
$\Rightarrow x^{3} - 6 x^{2} - 14 x - 8 = 0$ [Multiplying both sides by $- 1$ ]
It is not of the form $a x^{2} + b x + c = 0$
Hence, the given equation is not a quadratic equation.

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