Solve 22/7alpha^200alpha[(42/2)^2-(35/2)^2]

$$\frac { 22 } { 7 } \alpha ^ { 200 } \alpha [ ( \frac { 42 } { 2 } ) ^ { 2 } - ( \frac { 35 } { 2 } ) ^ { 2 } ]$$

Evaluate

$$\frac{847\alpha ^{201}}{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 200 and 1 to get 201.

$$\frac{22}{7}\alpha ^{201}\left(\left(\frac{42}{2}\right)^{2}-\left(\frac{35}{2}\right)^{2}\right)$$

Divide 42 by 2 to get 21.

$$\frac{22}{7}\alpha ^{201}\left(21^{2}-\left(\frac{35}{2}\right)^{2}\right)$$

Calculate 21 to the power of 2 and get 441.

$$\frac{22}{7}\alpha ^{201}\left(441-\left(\frac{35}{2}\right)^{2}\right)$$

Calculate \frac{35}{2} to the power of 2 and get \frac{1225}{4}.

$$\frac{22}{7}\alpha ^{201}\left(441-\frac{1225}{4}\right)$$

Subtract \frac{1225}{4} from 441 to get \frac{539}{4}.

$$\frac{22}{7}\alpha ^{201}\times \frac{539}{4}$$

Multiply \frac{22}{7} and \frac{539}{4} to get \frac{847}{2}.

$$\frac{847}{2}\alpha ^{201}$$

Expand

$$\frac{847\alpha ^{201}}{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 200 and 1 to get 201.

$$\frac{22}{7}\alpha ^{201}\left(\left(\frac{42}{2}\right)^{2}-\left(\frac{35}{2}\right)^{2}\right)$$

Divide 42 by 2 to get 21.

$$\frac{22}{7}\alpha ^{201}\left(21^{2}-\left(\frac{35}{2}\right)^{2}\right)$$

Calculate 21 to the power of 2 and get 441.

$$\frac{22}{7}\alpha ^{201}\left(441-\left(\frac{35}{2}\right)^{2}\right)$$

Calculate \frac{35}{2} to the power of 2 and get \frac{1225}{4}.

$$\frac{22}{7}\alpha ^{201}\left(441-\frac{1225}{4}\right)$$

Subtract \frac{1225}{4} from 441 to get \frac{539}{4}.

$$\frac{22}{7}\alpha ^{201}\times \frac{539}{4}$$

Multiply \frac{22}{7} and \frac{539}{4} to get \frac{847}{2}.

$$\frac{847}{2}\alpha ^{201}$$