Question

Solve the given equation.

${\mathit{x}}^{\mathbf{2}}\left(x+2\right)\mathbf{=}\mathit{x}\left(x^2+2x+1\right)$

Short answer

$\mathit{x}\mathbf{=}\mathbf{0}$ is the solution of the given equation.

Step-by-step solution

Step 1. Define an equation.

In mathematics, an equation is a statement that asserts the equality of two expressions, which are connected by the equal sign $"="$.

Step 2. Define the power of a product rule.

Power of a product rule states that if the two exponents of the same base are multiplied then the exponents are added and base remains the same.

$a^m.a^n=a^{m+n}$

Where,$a$ is any non-zero real number.

Step 3. Solve the equation, x2(x+2)=x(x2+2x+1).

Use the power of a product rule to solve the equation.

$\begin{array}{c}{x}^2\left(x+2\right)=x\left(x^2+2x+1\right)\\ x^2\left(x\right)+x^2\left(2\right)=x\left(x^2\right)+x\left(2x\right)+x\left(1\right)\\ x^3+2x^2=x^3+2x^2+x\\ x^3+2x^2+x-x^3+2x^2=0\\ x=0\end{array}$

Therefore,$x=0$ is the solution of the given equation.