Solve [(2+1/2)^{2}*(3-1/2)^2]*(5/2)^2[(-5/2)^2-(frac{5}{2})^2]-frac{5}{2}

$$[ ( 2 + \frac { 1 } { 2 } ) ^ { 2 } \cdot ( 3 - \frac { 1 } { 2 } ) ^ { 2 } ] \cdot ( \frac { 5 } { 2 } ) ^ { 2 } [ ( - \frac { 5 } { 2 } ) ^ { 2 } - ( \frac { 5 } { 2 } ) ^ { 2 } ] - \frac { 5 } { 2 }$$

Evaluate

$$-\frac{5}{2}=-2.5$$

Solution Steps

Add 2 and \frac{1}{2} to get \frac{5}{2}.

$$\left(\frac{5}{2}\right)^{2}\left(3-\frac{1}{2}\right)^{2}\times \left(\frac{5}{2}\right)^{2}\left(\left(-\frac{5}{2}\right)^{2}-\left(\frac{5}{2}\right)^{2}\right)-\frac{5}{2}$$

Calculate \frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$\frac{25}{4}\left(3-\frac{1}{2}\right)^{2}\times \left(\frac{5}{2}\right)^{2}\left(\left(-\frac{5}{2}\right)^{2}-\left(\frac{5}{2}\right)^{2}\right)-\frac{5}{2}$$

Subtract \frac{1}{2} from 3 to get \frac{5}{2}.

$$\frac{25}{4}\times \left(\frac{5}{2}\right)^{2}\times \left(\frac{5}{2}\right)^{2}\left(\left(-\frac{5}{2}\right)^{2}-\left(\frac{5}{2}\right)^{2}\right)-\frac{5}{2}$$

Calculate \frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$\frac{25}{4}\times \frac{25}{4}\times \left(\frac{5}{2}\right)^{2}\left(\left(-\frac{5}{2}\right)^{2}-\left(\frac{5}{2}\right)^{2}\right)-\frac{5}{2}$$

Multiply \frac{25}{4} and \frac{25}{4} to get \frac{625}{16}.

$$\frac{625}{16}\times \left(\frac{5}{2}\right)^{2}\left(\left(-\frac{5}{2}\right)^{2}-\left(\frac{5}{2}\right)^{2}\right)-\frac{5}{2}$$

Calculate \frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$\frac{625}{16}\times \frac{25}{4}\left(\left(-\frac{5}{2}\right)^{2}-\left(\frac{5}{2}\right)^{2}\right)-\frac{5}{2}$$

Multiply \frac{625}{16} and \frac{25}{4} to get \frac{15625}{64}.

$$\frac{15625}{64}\left(\left(-\frac{5}{2}\right)^{2}-\left(\frac{5}{2}\right)^{2}\right)-\frac{5}{2}$$

Calculate -\frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$\frac{15625}{64}\left(\frac{25}{4}-\left(\frac{5}{2}\right)^{2}\right)-\frac{5}{2}$$

Calculate \frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$\frac{15625}{64}\left(\frac{25}{4}-\frac{25}{4}\right)-\frac{5}{2}$$

Subtract \frac{25}{4} from \frac{25}{4} to get 0.

$$\frac{15625}{64}\times 0-\frac{5}{2}$$

Multiply \frac{15625}{64} and 0 to get 0.

$$0-\frac{5}{2}$$

Subtract \frac{5}{2} from 0 to get -\frac{5}{2}.

$$-\frac{5}{2}$$

Factor

$$-\frac{5}{2} = -2\frac{1}{2} = -2.5$$