Solve 991^2-992^2-993^2+994^2-{995}^2+{996}^2+{997}^2-{998}^2

$${ 991 }^{ 2 } - { 992 }^{ 2 } - { 993 }^{ 2 } + { 994 }^{ 2 } - { 995 }^{ 2 } + { 996 }^{ 2 } + { 997 }^{ 2 } - { 998 }^{ 2 }$$

Evaluate

$$0$$

Solution Steps

Calculate 991 to the power of 2 and get 982081.

$$982081-992^{2}-993^{2}+994^{2}-995^{2}+996^{2}+997^{2}-998^{2}$$

Calculate 992 to the power of 2 and get 984064.

$$982081-984064-993^{2}+994^{2}-995^{2}+996^{2}+997^{2}-998^{2}$$

Subtract 984064 from 982081 to get -1983.

$$-1983-993^{2}+994^{2}-995^{2}+996^{2}+997^{2}-998^{2}$$

Calculate 993 to the power of 2 and get 986049.

$$-1983-986049+994^{2}-995^{2}+996^{2}+997^{2}-998^{2}$$

Subtract 986049 from -1983 to get -988032.

$$-988032+994^{2}-995^{2}+996^{2}+997^{2}-998^{2}$$

Calculate 994 to the power of 2 and get 988036.

$$-988032+988036-995^{2}+996^{2}+997^{2}-998^{2}$$

Add -988032 and 988036 to get 4.

$$4-995^{2}+996^{2}+997^{2}-998^{2}$$

Calculate 995 to the power of 2 and get 990025.

$$4-990025+996^{2}+997^{2}-998^{2}$$

Subtract 990025 from 4 to get -990021.

$$-990021+996^{2}+997^{2}-998^{2}$$

Calculate 996 to the power of 2 and get 992016.

$$-990021+992016+997^{2}-998^{2}$$

Add -990021 and 992016 to get 1995.

$$1995+997^{2}-998^{2}$$

Calculate 997 to the power of 2 and get 994009.

$$1995+994009-998^{2}$$

Add 1995 and 994009 to get 996004.

$$996004-998^{2}$$

Calculate 998 to the power of 2 and get 996004.

$$996004-996004$$

Subtract 996004 from 996004 to get 0.

$$0$$

Factor

$$0$$