Solve 2020^2-2018^2+2016^2-2014^2+{2012}^{2}-{2010}^{2}+{2008}^{2}-{2006}^{2}+{2004}^2-{2002}^2+{2000}^2-{1998}^2

$${ 2020 }^{ 2 } - { 2018 }^{ 2 } + { 2016 }^{ 2 } - { 2014 }^{ 2 } + { 2012 }^{ 2 } - { 2010 }^{ 2 } + { 2008 }^{ 2 } - { 2006 }^{ 2 } + { 2004 }^{ 2 } - { 2002 }^{ 2 } + { 2000 }^{ 2 } - { 1998 }^{ 2 }$$

Evaluate

$$48216$$

Solution Steps

Calculate 2020 to the power of 2 and get 4080400.

$$4080400-2018^{2}+2016^{2}-2014^{2}+2012^{2}-2010^{2}+2008^{2}-2006^{2}+2004^{2}-2002^{2}+2000^{2}-1998^{2}$$

Calculate 2018 to the power of 2 and get 4072324.

$$4080400-4072324+2016^{2}-2014^{2}+2012^{2}-2010^{2}+2008^{2}-2006^{2}+2004^{2}-2002^{2}+2000^{2}-1998^{2}$$

Subtract 4072324 from 4080400 to get 8076.

$$8076+2016^{2}-2014^{2}+2012^{2}-2010^{2}+2008^{2}-2006^{2}+2004^{2}-2002^{2}+2000^{2}-1998^{2}$$

Calculate 2016 to the power of 2 and get 4064256.

$$8076+4064256-2014^{2}+2012^{2}-2010^{2}+2008^{2}-2006^{2}+2004^{2}-2002^{2}+2000^{2}-1998^{2}$$

Add 8076 and 4064256 to get 4072332.

$$4072332-2014^{2}+2012^{2}-2010^{2}+2008^{2}-2006^{2}+2004^{2}-2002^{2}+2000^{2}-1998^{2}$$

Calculate 2014 to the power of 2 and get 4056196.

$$4072332-4056196+2012^{2}-2010^{2}+2008^{2}-2006^{2}+2004^{2}-2002^{2}+2000^{2}-1998^{2}$$

Subtract 4056196 from 4072332 to get 16136.

$$16136+2012^{2}-2010^{2}+2008^{2}-2006^{2}+2004^{2}-2002^{2}+2000^{2}-1998^{2}$$

Calculate 2012 to the power of 2 and get 4048144.

$$16136+4048144-2010^{2}+2008^{2}-2006^{2}+2004^{2}-2002^{2}+2000^{2}-1998^{2}$$

Add 16136 and 4048144 to get 4064280.

$$4064280-2010^{2}+2008^{2}-2006^{2}+2004^{2}-2002^{2}+2000^{2}-1998^{2}$$

Calculate 2010 to the power of 2 and get 4040100.

$$4064280-4040100+2008^{2}-2006^{2}+2004^{2}-2002^{2}+2000^{2}-1998^{2}$$

Subtract 4040100 from 4064280 to get 24180.

$$24180+2008^{2}-2006^{2}+2004^{2}-2002^{2}+2000^{2}-1998^{2}$$

Calculate 2008 to the power of 2 and get 4032064.

$$24180+4032064-2006^{2}+2004^{2}-2002^{2}+2000^{2}-1998^{2}$$

Add 24180 and 4032064 to get 4056244.

$$4056244-2006^{2}+2004^{2}-2002^{2}+2000^{2}-1998^{2}$$

Calculate 2006 to the power of 2 and get 4024036.

$$4056244-4024036+2004^{2}-2002^{2}+2000^{2}-1998^{2}$$

Subtract 4024036 from 4056244 to get 32208.

$$32208+2004^{2}-2002^{2}+2000^{2}-1998^{2}$$

Calculate 2004 to the power of 2 and get 4016016.

$$32208+4016016-2002^{2}+2000^{2}-1998^{2}$$

Add 32208 and 4016016 to get 4048224.

$$4048224-2002^{2}+2000^{2}-1998^{2}$$

Calculate 2002 to the power of 2 and get 4008004.

$$4048224-4008004+2000^{2}-1998^{2}$$

Subtract 4008004 from 4048224 to get 40220.

$$40220+2000^{2}-1998^{2}$$

Calculate 2000 to the power of 2 and get 4000000.

$$40220+4000000-1998^{2}$$

Add 40220 and 4000000 to get 4040220.

$$4040220-1998^{2}$$

Calculate 1998 to the power of 2 and get 3992004.

$$4040220-3992004$$

Subtract 3992004 from 4040220 to get 48216.

$$48216$$

Factor

$$2^{3}\times 3\times 7^{2}\times 41$$