a, - Ta có :
$A = 2011 × 2011$
$= (2010 + 1) × 2011$
$= 2010 × 2011 + 1 × 2011$
$= 2010 × (2012 - 1) + 2011$
$= 2010 × 2012 - 2010 × 1 + 2011$
$= 2010 × 2012 + (2011 - 2010)$
$= 2010 × 2012 + 1$
- Vì $2010 × 2012 + 1$ $>$ $2010 × 2012$ => $A > B$
b, - Ta có :
$A = 2018 × 2020 $
$= (2019 - 1) × 2020$
$= 2019 × 2020 - 1 × 2020$
$= 2019 × (2019 + 1) - 2020 $
$= 2019 × 2019 + 1 × 2019 - 2020$
$= 2019 × 2019 - (2020 - 2019)$
$= 2019 × 2019 - 1$
- Vì $2019 × 2019 - 1$ $<$ $2019 × 2019$ => $A < B$