Question

Simplify ${\left(x+2\right)}^3=2x\left(x^2-1\right)$ and check whether it is a quadratic equation

Answer 1

Step 1: Finding the simplest form

Consider ${\left(x+2\right)}^3=2x\left(x^2-1\right)$

We know that ${\left(a+b\right)}^3=a^3+b^3+3a^{2}b+3a{b}^2$

$$\begin{gathered} {\left(x+2\right)}^3=2x\left(x^2-1\right) \\ {x}^3+2^3+3\left(x^2\right)\left(2\right)+3\left(x\right)\left(2^2\right)=2x^3-2x \\ {x}^3+8+6x^2+3\left(x\right)\left(4\right)-2x^3+2x=0 \\ {x}^3+8+6x^2+12x-2x^3+2x=0 \\ -x^3+8+6x^2+14x=0 \\ -x^3+6x^2+14x+8=0 \end{gathered}$$

Hence, ${\left(x+2\right)}^3=2x\left(x^2-1\right)$ is $-x^3+6x^2+14x+8=0$

Step 2: Find whether the equation is quadratic or not

To check whether the equation is quadratic or not

Consider $-x^3+6x^2+14x+8=0$

Since the equation has degree $3$.

Hence, $-x^3+6x^2+14x+8=0$ not a quadratic equation.