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Check whether the following is the quadratic equations:

(x + 2)^{3} = 2x(x^{2} - 1)

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#### Solution

(x + 2)^{3} = 2x(x^{2} - 1)

⇒ x^{3} + 3x^{2}(2) + 3x(2)^{2} + (2)^{3} = 2x^{3} - 2x

⇒ x^{3 }+ 6x^{2} + 12x + 8 = 2x^{3} - 2x

⇒ x^{3} +6x^{2} +12x + 8 -2x^{3} + 2x = 0

⇒ - x^{3} + 6x^{2} + 14x + 8 = 0

It is not of the form ax^{2} + bx + c = 0.

Hence, the given equation is not a quadratic equation.

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