Solve 12/5(-12/5x+12/7x^{2}-12/11x^3)+(-frac{5}{3}x+frac{7}{11}x^3-frac{1}{2}x^2)-(frac{3}{14}x^2-frac{1}{15}x)

$$\frac { 12 } { 5 } ( - \frac { 12 } { 5 } x + \frac { 12 } { 7 } x ^ { 2 } - \frac { 12 } { 11 } x ^ { 3 } ) + ( - \frac { 5 } { 3 } x + \frac { 7 } { 11 } x ^ { 3 } - \frac { 1 } { 2 } x ^ { 2 } ) - ( \frac { 3 } { 14 } x ^ { 2 } - \frac { 1 } { 15 } x )$$

Evaluate

$$-\frac{109x^{3}}{55}+\frac{17x^{2}}{5}-\frac{184x}{25}$$

Solution Steps

Use the distributive property to multiply \frac{12}{5} by -\frac{12}{5}x+\frac{12}{7}x^{2}-\frac{12}{11}x^{3}.

$$-\frac{144}{25}x+\frac{144}{35}x^{2}-\frac{144}{55}x^{3}-\frac{5}{3}x+\frac{7}{11}x^{3}-\frac{1}{2}x^{2}-\left(\frac{3}{14}x^{2}-\frac{1}{15}x\right)$$

Combine -\frac{144}{25}x and -\frac{5}{3}x to get -\frac{557}{75}x.

$$-\frac{557}{75}x+\frac{144}{35}x^{2}-\frac{144}{55}x^{3}+\frac{7}{11}x^{3}-\frac{1}{2}x^{2}-\left(\frac{3}{14}x^{2}-\frac{1}{15}x\right)$$

Combine -\frac{144}{55}x^{3} and \frac{7}{11}x^{3} to get -\frac{109}{55}x^{3}.

$$-\frac{557}{75}x+\frac{144}{35}x^{2}-\frac{109}{55}x^{3}-\frac{1}{2}x^{2}-\left(\frac{3}{14}x^{2}-\frac{1}{15}x\right)$$

Combine \frac{144}{35}x^{2} and -\frac{1}{2}x^{2} to get \frac{253}{70}x^{2}.

$$-\frac{557}{75}x+\frac{253}{70}x^{2}-\frac{109}{55}x^{3}-\left(\frac{3}{14}x^{2}-\frac{1}{15}x\right)$$

To find the opposite of \frac{3}{14}x^{2}-\frac{1}{15}x, find the opposite of each term.

$$-\frac{557}{75}x+\frac{253}{70}x^{2}-\frac{109}{55}x^{3}-\frac{3}{14}x^{2}+\frac{1}{15}x$$

Combine \frac{253}{70}x^{2} and -\frac{3}{14}x^{2} to get \frac{17}{5}x^{2}.

$$-\frac{557}{75}x+\frac{17}{5}x^{2}-\frac{109}{55}x^{3}+\frac{1}{15}x$$

Combine -\frac{557}{75}x and \frac{1}{15}x to get -\frac{184}{25}x.

$$-\frac{184}{25}x+\frac{17}{5}x^{2}-\frac{109}{55}x^{3}$$

Expand

$$-\frac{109x^{3}}{55}+\frac{17x^{2}}{5}-\frac{184x}{25}$$

Solution Steps

Use the distributive property to multiply \frac{12}{5} by -\frac{12}{5}x+\frac{12}{7}x^{2}-\frac{12}{11}x^{3}.

$$-\frac{144}{25}x+\frac{144}{35}x^{2}-\frac{144}{55}x^{3}-\frac{5}{3}x+\frac{7}{11}x^{3}-\frac{1}{2}x^{2}-\left(\frac{3}{14}x^{2}-\frac{1}{15}x\right)$$

Combine -\frac{144}{25}x and -\frac{5}{3}x to get -\frac{557}{75}x.

$$-\frac{557}{75}x+\frac{144}{35}x^{2}-\frac{144}{55}x^{3}+\frac{7}{11}x^{3}-\frac{1}{2}x^{2}-\left(\frac{3}{14}x^{2}-\frac{1}{15}x\right)$$

Combine -\frac{144}{55}x^{3} and \frac{7}{11}x^{3} to get -\frac{109}{55}x^{3}.

$$-\frac{557}{75}x+\frac{144}{35}x^{2}-\frac{109}{55}x^{3}-\frac{1}{2}x^{2}-\left(\frac{3}{14}x^{2}-\frac{1}{15}x\right)$$

Combine \frac{144}{35}x^{2} and -\frac{1}{2}x^{2} to get \frac{253}{70}x^{2}.

$$-\frac{557}{75}x+\frac{253}{70}x^{2}-\frac{109}{55}x^{3}-\left(\frac{3}{14}x^{2}-\frac{1}{15}x\right)$$

To find the opposite of \frac{3}{14}x^{2}-\frac{1}{15}x, find the opposite of each term.

$$-\frac{557}{75}x+\frac{253}{70}x^{2}-\frac{109}{55}x^{3}-\frac{3}{14}x^{2}+\frac{1}{15}x$$

Combine \frac{253}{70}x^{2} and -\frac{3}{14}x^{2} to get \frac{17}{5}x^{2}.

$$-\frac{557}{75}x+\frac{17}{5}x^{2}-\frac{109}{55}x^{3}+\frac{1}{15}x$$

Combine -\frac{557}{75}x and \frac{1}{15}x to get -\frac{184}{25}x.

$$-\frac{184}{25}x+\frac{17}{5}x^{2}-\frac{109}{55}x^{3}$$