Solve (-2/3x[(3/5x^2+15x)+14/3x(36/3x^4-5x)-frac{25}{2}x^2])

$$( - \frac { 2 } { 3 } x [ ( \frac { 3 } { 5 } x ^ { 2 } + 15 x ) + \frac { 14 } { 3 } x ( \frac { 36 } { 3 } x ^ { 4 } - 5 x ) - \frac { 25 } { 2 } x ^ { 2 } ] )$$

Evaluate

$$-\frac{112x^{6}}{3}+\frac{1057x^{3}}{45}-10x^{2}$$

Solution Steps

Divide 36 by 3 to get 12.

$$-\frac{2}{3}x\left(\frac{3}{5}x^{2}+15x+\frac{14}{3}x\left(12x^{4}-5x\right)-\frac{25}{2}x^{2}\right)$$

Use the distributive property to multiply \frac{14}{3}x by 12x^{4}-5x.

$$-\frac{2}{3}x\left(\frac{3}{5}x^{2}+15x+56x^{5}-\frac{70}{3}x^{2}-\frac{25}{2}x^{2}\right)$$

Combine \frac{3}{5}x^{2} and -\frac{70}{3}x^{2} to get -\frac{341}{15}x^{2}.

$$-\frac{2}{3}x\left(-\frac{341}{15}x^{2}+15x+56x^{5}-\frac{25}{2}x^{2}\right)$$

Combine -\frac{341}{15}x^{2} and -\frac{25}{2}x^{2} to get -\frac{1057}{30}x^{2}.

$$-\frac{2}{3}x\left(-\frac{1057}{30}x^{2}+15x+56x^{5}\right)$$

Use the distributive property to multiply -\frac{2}{3}x by -\frac{1057}{30}x^{2}+15x+56x^{5}.

$$\frac{1057}{45}x^{3}-10x^{2}-\frac{112}{3}x^{6}$$

Expand

$$-\frac{112x^{6}}{3}+\frac{1057x^{3}}{45}-10x^{2}$$

Solution Steps

Divide 36 by 3 to get 12.

$$-\frac{2}{3}x\left(\frac{3}{5}x^{2}+15x+\frac{14}{3}x\left(12x^{4}-5x\right)-\frac{25}{2}x^{2}\right)$$

Use the distributive property to multiply \frac{14}{3}x by 12x^{4}-5x.

$$-\frac{2}{3}x\left(\frac{3}{5}x^{2}+15x+56x^{5}-\frac{70}{3}x^{2}-\frac{25}{2}x^{2}\right)$$

Combine \frac{3}{5}x^{2} and -\frac{70}{3}x^{2} to get -\frac{341}{15}x^{2}.

$$-\frac{2}{3}x\left(-\frac{341}{15}x^{2}+15x+56x^{5}-\frac{25}{2}x^{2}\right)$$

Combine -\frac{341}{15}x^{2} and -\frac{25}{2}x^{2} to get -\frac{1057}{30}x^{2}.

$$-\frac{2}{3}x\left(-\frac{1057}{30}x^{2}+15x+56x^{5}\right)$$

Use the distributive property to multiply -\frac{2}{3}x by -\frac{1057}{30}x^{2}+15x+56x^{5}.

$$\frac{1057}{45}x^{3}-10x^{2}-\frac{112}{3}x^{6}$$