Solve 4!/2!*2!-1*8!/2!-1*8!/2!+7!/2!

$$\frac { 4 ! } { 2 ! \times 2 ! } - 1 \times \frac { 8 ! } { 2 ! } - 1 \times \frac { 8 ! } { 2 ! } + \frac { 7 ! } { 2 ! }$$

Evaluate

$$-37794$$

Solution Steps

Multiply 2! and 2! to get \left(2!\right)^{2}.

$$\frac{4!}{\left(2!\right)^{2}}-1\times \frac{8!}{2!}-1\times \frac{8!}{2!}+\frac{7!}{2!}$$

The factorial of 4 is 24.

$$\frac{24}{\left(2!\right)^{2}}-1\times \frac{8!}{2!}-1\times \frac{8!}{2!}+\frac{7!}{2!}$$

The factorial of 2 is 2.

$$\frac{24}{2^{2}}-1\times \frac{8!}{2!}-1\times \frac{8!}{2!}+\frac{7!}{2!}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{24}{4}-1\times \frac{8!}{2!}-1\times \frac{8!}{2!}+\frac{7!}{2!}$$

Divide 24 by 4 to get 6.

$$6-1\times \frac{8!}{2!}-1\times \frac{8!}{2!}+\frac{7!}{2!}$$

The factorial of 8 is 40320.

$$6-1\times \frac{40320}{2!}-1\times \frac{8!}{2!}+\frac{7!}{2!}$$

The factorial of 2 is 2.

$$6-1\times \frac{40320}{2}-1\times \frac{8!}{2!}+\frac{7!}{2!}$$

Divide 40320 by 2 to get 20160.

$$6-1\times 20160-1\times \frac{8!}{2!}+\frac{7!}{2!}$$

Multiply 1 and 20160 to get 20160.

$$6-20160-1\times \frac{8!}{2!}+\frac{7!}{2!}$$

Subtract 20160 from 6 to get -20154.

$$-20154-1\times \frac{8!}{2!}+\frac{7!}{2!}$$

The factorial of 8 is 40320.

$$-20154-1\times \frac{40320}{2!}+\frac{7!}{2!}$$

The factorial of 2 is 2.

$$-20154-1\times \frac{40320}{2}+\frac{7!}{2!}$$

Divide 40320 by 2 to get 20160.

$$-20154-1\times 20160+\frac{7!}{2!}$$

Multiply 1 and 20160 to get 20160.

$$-20154-20160+\frac{7!}{2!}$$

Subtract 20160 from -20154 to get -40314.

$$-40314+\frac{7!}{2!}$$

The factorial of 7 is 5040.

$$-40314+\frac{5040}{2!}$$

The factorial of 2 is 2.

$$-40314+\frac{5040}{2}$$

Divide 5040 by 2 to get 2520.

$$-40314+2520$$

Add -40314 and 2520 to get -37794.

$$-37794$$

Factor

$$-37794$$