Solve f(x)=-x^3/3+4x^2

$$f ( x ) = - \frac { x ^ { 3 } } { 3 } + 4 x ^ { 2 }$$

Evaluate

$$\frac{\left(12-x\right)x^{2}}{3}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4x^{2} times \frac{3}{3}.

$$-\frac{x^{3}}{3}+\frac{3\times 4x^{2}}{3}$$

Since -\frac{x^{3}}{3} and \frac{3\times 4x^{2}}{3} have the same denominator, add them by adding their numerators.

$$\frac{-x^{3}+3\times 4x^{2}}{3}$$

Do the multiplications in -x^{3}+3\times 4x^{2}.

$$\frac{-x^{3}+12x^{2}}{3}$$

Factor

$$\frac{\left(12-x\right)x^{2}}{3}$$

Solution Steps

Factor out \frac{1}{3}.

$$\frac{-x^{3}+12x^{2}}{3}$$

Consider -x^{3}+12x^{2}. Factor out x^{2}.

$$x^{2}\left(-x+12\right)$$

Rewrite the complete factored expression.

$$\frac{x^{2}\left(-x+12\right)}{3}$$