Solve x^2/2+x^3/43

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

Evaluate

$$\frac{\left(3x+2\right)x^{2}}{4}$$

Solution Steps

Express \frac{x^{3}}{4}\times 3 as a single fraction.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 4 is 4. Multiply \frac{x^{2}}{2} times \frac{2}{2}.

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

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

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

Factor

$$\frac{\left(3x+2\right)x^{2}}{4}$$

Solution Steps

Factor out \frac{1}{4}.

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

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

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

Rewrite the complete factored expression.

$$\frac{x^{2}\left(3x+2\right)}{4}$$