Question

Simplify $(x+2{)}^3=2x(x^2-1)$ and check whether its is a quadratic equation.

Answer 1

We know that the general form of quadratic equation is $a{x}^2+bx+c=0$.

The given equation is $(x+2{)}^3=2x(x^2-1)$ can be simplified as follows:

$(x+2{)}^3=2x(x^2-1)\Rightarrow x^3+2^3+(3\times x\times 2\left)\right(x+2)=2x^3-2x(\because (a+b{)}^3=a^3+b^3+3ab(a+b\left)\right)\Rightarrow x^3+8+6x(x+2)=2x^3-2x\Rightarrow x^3+8+6x^2+12x=2x^3-2x\Rightarrow x^3+8+6x^2+12x-2x^3+2x=0\Rightarrow -x^3+6x^2+14x+8=0$

Since the variable $x$ in the equation $-x^3+6x^2+14x+8=0$ has degree $3$, therefore, it is not of the form $a{x}^2+bx+c=0$.

Hence, the equation $(x+2{)}^3=2x(x^2-1)$ is not a quadratic equation.