Find the value of the following expression.
( 2 0 1 9 + 2 0 1 9 ) + ( 2 0 1 9 − 2 0 1 9 ) + ( 2 0 1 9 × 2 0 1 9 ) + ( 2 0 1 9 ÷ 2 0 1 9 )
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FullSimplify [ ( n − n ) + n n + n n + ( n + n ) ] ⇒ ( n + 1 ) 2 ⇒ ± ∣ ∣ n + 1 ∣ ∣
± 2 0 2 0
Take n as 2019, and then simplify. That will become:
( n + n ) + ( n − n ) + ( n × n ) + ( n / n ) = ( 2 n ) ( n 2 ) f a c t o r i z e = ( 1 + n ) 2 = ± n + 1 = ± 2 0 2 0
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The expression is equal to 2 0 1 9 2 + 2 ⋅ 2 0 1 9 + 1 = ( 2 0 1 9 + 1 ) 2 = 2 0 2 0 .