Simplify and check if the following equation is a Quadratic equation.
$(x + 5)^{3} = x^{3} - 8$

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Solution

$(x + 5)^{3} = x^{3} - 8$

$x^{3} + 3 (5) (x + 5) + 125 = x^{3} - 8$

$x^{3} + 15 x^{2} + 75 x + 125 = x^{3} - 8$

$15 x^{2} + 75 x + 133 = 0$

Yes, it is quadratic as the highest power of $x = 2$ .

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