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

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

Avaliar

$$48216$$

Passos Para a Resolução

Calcule 2020 elevado a 2 e obtenha 4080400.

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

Calcule 2018 elevado a 2 e obtenha 4072324.

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

Subtraia 4072324 de 4080400 para obter 8076.

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

Calcule 2016 elevado a 2 e obtenha 4064256.

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

Some 8076 e 4064256 para obter 4072332.

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

Calcule 2014 elevado a 2 e obtenha 4056196.

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

Subtraia 4056196 de 4072332 para obter 16136.

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

Calcule 2012 elevado a 2 e obtenha 4048144.

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

Some 16136 e 4048144 para obter 4064280.

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

Calcule 2010 elevado a 2 e obtenha 4040100.

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

Subtraia 4040100 de 4064280 para obter 24180.

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

Calcule 2008 elevado a 2 e obtenha 4032064.

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

Some 24180 e 4032064 para obter 4056244.

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

Calcule 2006 elevado a 2 e obtenha 4024036.

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

Subtraia 4024036 de 4056244 para obter 32208.

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

Calcule 2004 elevado a 2 e obtenha 4016016.

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

Some 32208 e 4016016 para obter 4048224.

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

Calcule 2002 elevado a 2 e obtenha 4008004.

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

Subtraia 4008004 de 4048224 para obter 40220.

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

Calcule 2000 elevado a 2 e obtenha 4000000.

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

Some 40220 e 4000000 para obter 4040220.

$$4040220-1998^{2}$$

Calcule 1998 elevado a 2 e obtenha 3992004.

$$4040220-3992004$$

Subtraia 3992004 de 4040220 para obter 48216.

$$48216$$

Fatorizar

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