Solve 2/3x*(1/4a-3/2x)-5/7a*(frac{2}{10}x-frac{7}{3}a)-frac{10}{9}*(-frac{9}{20}x^2+frac{3}{2}a^2)+frac{5}{42}ax=

$$\frac { 2 } { 3 } x \cdot ( \frac { 1 } { 4 } a - \frac { 3 } { 2 } x ) - \frac { 5 } { 7 } a \cdot ( \frac { 2 } { 10 } x - \frac { 7 } { 3 } a ) - \frac { 10 } { 9 } \cdot ( - \frac { 9 } { 20 } x ^ { 2 } + \frac { 3 } { 2 } a ^ { 2 } ) + \frac { 5 } { 42 } a x =$$

Evaluate

$$\frac{ax}{7}-\frac{x^{2}}{2}$$

Solution Steps

Use the distributive property to multiply \frac{2}{3}x by \frac{1}{4}a-\frac{3}{2}x.

$$\frac{1}{6}xa-x^{2}-\frac{5}{7}a\left(\frac{2}{10}x-\frac{7}{3}a\right)-\frac{10}{9}\left(-\frac{9}{20}x^{2}+\frac{3}{2}a^{2}\right)+\frac{5}{42}ax$$

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{1}{6}xa-x^{2}-\frac{5}{7}a\left(\frac{1}{5}x-\frac{7}{3}a\right)-\frac{10}{9}\left(-\frac{9}{20}x^{2}+\frac{3}{2}a^{2}\right)+\frac{5}{42}ax$$

Use the distributive property to multiply -\frac{10}{9} by -\frac{9}{20}x^{2}+\frac{3}{2}a^{2}.

$$\frac{1}{6}xa-x^{2}-\frac{5}{7}a\left(\frac{1}{5}x-\frac{7}{3}a\right)+\frac{1}{2}x^{2}-\frac{5}{3}a^{2}+\frac{5}{42}ax$$

Use the distributive property to multiply -\frac{5}{7}a by \frac{1}{5}x-\frac{7}{3}a.

$$\frac{1}{6}xa-x^{2}-\frac{1}{7}ax+\frac{5}{3}a^{2}+\frac{1}{2}x^{2}-\frac{5}{3}a^{2}+\frac{5}{42}ax$$

Combine \frac{1}{6}xa and -\frac{1}{7}ax to get \frac{1}{42}xa.

$$\frac{1}{42}xa-x^{2}+\frac{5}{3}a^{2}+\frac{1}{2}x^{2}-\frac{5}{3}a^{2}+\frac{5}{42}ax$$

Combine -x^{2} and \frac{1}{2}x^{2} to get -\frac{1}{2}x^{2}.

$$\frac{1}{42}xa-\frac{1}{2}x^{2}+\frac{5}{3}a^{2}-\frac{5}{3}a^{2}+\frac{5}{42}ax$$

Combine \frac{5}{3}a^{2} and -\frac{5}{3}a^{2} to get 0.

$$\frac{1}{42}xa-\frac{1}{2}x^{2}+\frac{5}{42}ax$$

Combine \frac{1}{42}xa and \frac{5}{42}ax to get \frac{1}{7}xa.

$$\frac{1}{7}xa-\frac{1}{2}x^{2}$$

Expand

$$\frac{ax}{7}-\frac{x^{2}}{2}$$

Solution Steps

Use the distributive property to multiply \frac{2}{3}x by \frac{1}{4}a-\frac{3}{2}x.

$$\frac{1}{6}xa-x^{2}-\frac{5}{7}a\left(\frac{2}{10}x-\frac{7}{3}a\right)-\frac{10}{9}\left(-\frac{9}{20}x^{2}+\frac{3}{2}a^{2}\right)+\frac{5}{42}ax$$

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{1}{6}xa-x^{2}-\frac{5}{7}a\left(\frac{1}{5}x-\frac{7}{3}a\right)-\frac{10}{9}\left(-\frac{9}{20}x^{2}+\frac{3}{2}a^{2}\right)+\frac{5}{42}ax$$

Use the distributive property to multiply -\frac{10}{9} by -\frac{9}{20}x^{2}+\frac{3}{2}a^{2}.

$$\frac{1}{6}xa-x^{2}-\frac{5}{7}a\left(\frac{1}{5}x-\frac{7}{3}a\right)+\frac{1}{2}x^{2}-\frac{5}{3}a^{2}+\frac{5}{42}ax$$

Use the distributive property to multiply -\frac{5}{7}a by \frac{1}{5}x-\frac{7}{3}a.

$$\frac{1}{6}xa-x^{2}-\frac{1}{7}ax+\frac{5}{3}a^{2}+\frac{1}{2}x^{2}-\frac{5}{3}a^{2}+\frac{5}{42}ax$$

Combine \frac{1}{6}xa and -\frac{1}{7}ax to get \frac{1}{42}xa.

$$\frac{1}{42}xa-x^{2}+\frac{5}{3}a^{2}+\frac{1}{2}x^{2}-\frac{5}{3}a^{2}+\frac{5}{42}ax$$

Combine -x^{2} and \frac{1}{2}x^{2} to get -\frac{1}{2}x^{2}.

$$\frac{1}{42}xa-\frac{1}{2}x^{2}+\frac{5}{3}a^{2}-\frac{5}{3}a^{2}+\frac{5}{42}ax$$

Combine \frac{5}{3}a^{2} and -\frac{5}{3}a^{2} to get 0.

$$\frac{1}{42}xa-\frac{1}{2}x^{2}+\frac{5}{42}ax$$

Combine \frac{1}{42}xa and \frac{5}{42}ax to get \frac{1}{7}xa.

$$\frac{1}{7}xa-\frac{1}{2}x^{2}$$