Solve 1/3x*x*x-2x^2+3x

$$\frac{ 1 }{ 3 } x \times x \times x-2 { x }^{ 2 } +3x$$

Evaluate

$$\frac{x\left(x-3\right)^{2}}{3}$$

Solution Steps

Multiply x and x to get x^{2}.

$$\frac{1}{3}x^{2}x-2x^{2}+3x$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{1}{3}x^{3}-2x^{2}+3x$$

Factor

$$\frac{x\left(x-3\right)^{2}}{3}$$

Solution Steps

Factor out \frac{1}{3}.

$$\frac{xxx-6x^{2}+9x}{3}$$

Consider x^{3}-6x^{2}+9x. Factor out x.

$$x\left(x^{2}-6x+9\right)$$

Consider x^{2}-6x+9. Use the perfect square formula, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, where a=x and b=3.

$$\left(x-3\right)^{2}$$

Rewrite the complete factored expression.

$$\frac{x\left(x-3\right)^{2}}{3}$$