Just Factorize

Algebra Level 2

2016 2 + 2015 × 2017 − 2 × 2014 × 2018 = ? { 2016 }^{ 2 }+2015\times 2017-2\times 2014\times 2018=\, ?

2016 1 1008 7 0 10

Mateo Matijasevick by Mateo Matijasevick , 22, Colombia

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1 solution

In general, n 2 + ( n + 1 ) ( n − 1 ) − 2 ( n − 2 ) ( n + 2 ) = n 2 + n 2 − 1 − 2 n 2 + 8 = 7 { n }^{ 2 }+(n+1)(n-1)-2(n-2)(n+2)={ n }^{ 2 }+{ n }^{ 2 }-1-2{ n }^{ 2 }+8=7

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