Solve (x^2-1/2ax)-(2+3/2ax-1/4x^2)-5/4x^2+(2+frac{3}{2}ax)-frac{1}{3}ax

$$( x ^ { 2 } - \frac { 1 } { 2 } a x ) - ( 2 + \frac { 3 } { 2 } a x - \frac { 1 } { 4 } x ^ { 2 } ) - \frac { 5 } { 4 } x ^ { 2 } + ( 2 + \frac { 3 } { 2 } a x ) - \frac { 1 } { 3 } a x$$

Evaluate

$$-\frac{5ax}{6}$$

Solution Steps

To find the opposite of 2+\frac{3}{2}ax-\frac{1}{4}x^{2}, find the opposite of each term.

$$x^{2}-\frac{1}{2}ax-2-\frac{3}{2}ax+\frac{1}{4}x^{2}-\frac{5}{4}x^{2}+2+\frac{3}{2}ax-\frac{1}{3}ax$$

Combine -\frac{1}{2}ax and -\frac{3}{2}ax to get -2ax.

$$x^{2}-2ax-2+\frac{1}{4}x^{2}-\frac{5}{4}x^{2}+2+\frac{3}{2}ax-\frac{1}{3}ax$$

Combine x^{2} and \frac{1}{4}x^{2} to get \frac{5}{4}x^{2}.

$$\frac{5}{4}x^{2}-2ax-2-\frac{5}{4}x^{2}+2+\frac{3}{2}ax-\frac{1}{3}ax$$

Combine \frac{5}{4}x^{2} and -\frac{5}{4}x^{2} to get 0.

$$-2ax-2+2+\frac{3}{2}ax-\frac{1}{3}ax$$

Add -2 and 2 to get 0.

$$-2ax+\frac{3}{2}ax-\frac{1}{3}ax$$

Combine -2ax and \frac{3}{2}ax to get -\frac{1}{2}ax.

$$-\frac{1}{2}ax-\frac{1}{3}ax$$

Combine -\frac{1}{2}ax and -\frac{1}{3}ax to get -\frac{5}{6}ax.

$$-\frac{5}{6}ax$$

Expand

$$-\frac{5ax}{6}$$

Solution Steps

To find the opposite of 2+\frac{3}{2}ax-\frac{1}{4}x^{2}, find the opposite of each term.

$$x^{2}-\frac{1}{2}ax-2-\frac{3}{2}ax+\frac{1}{4}x^{2}-\frac{5}{4}x^{2}+2+\frac{3}{2}ax-\frac{1}{3}ax$$

Combine -\frac{1}{2}ax and -\frac{3}{2}ax to get -2ax.

$$x^{2}-2ax-2+\frac{1}{4}x^{2}-\frac{5}{4}x^{2}+2+\frac{3}{2}ax-\frac{1}{3}ax$$

Combine x^{2} and \frac{1}{4}x^{2} to get \frac{5}{4}x^{2}.

$$\frac{5}{4}x^{2}-2ax-2-\frac{5}{4}x^{2}+2+\frac{3}{2}ax-\frac{1}{3}ax$$

Combine \frac{5}{4}x^{2} and -\frac{5}{4}x^{2} to get 0.

$$-2ax-2+2+\frac{3}{2}ax-\frac{1}{3}ax$$

Add -2 and 2 to get 0.

$$-2ax+\frac{3}{2}ax-\frac{1}{3}ax$$

Combine -2ax and \frac{3}{2}ax to get -\frac{1}{2}ax.

$$-\frac{1}{2}ax-\frac{1}{3}ax$$

Combine -\frac{1}{2}ax and -\frac{1}{3}ax to get -\frac{5}{6}ax.

$$-\frac{5}{6}ax$$