Đáp án đúng:

Phương pháp giải:

Sử dụng tính chất kết hợp, phân phối của phép cộng và phép nhân.Giải chi tiết:a) \(\begin{array}{l}\,\,\,\,\,2020.2020 - 2022.2018\\ = 2020.\left( {2018 + 2} \right) - \left( {2020 + 2} \right).2018\\ = \left( {2020.2018 + 2020.2} \right) - \left( {2020.2018 + 2.2018} \right)\\ = 2020.2018 + 2020.2 - 2020.2018 - 2.2018\\ = \left( {2020.2018 - 2020.2018} \right) + \left( {2020.2 - 2.2018} \right)\\ = 0 + 2.\left( {2020 - 2018} \right)\\ = 0 + 2.2\\ = 4\end{array}\)b) \(\begin{array}{l}\,\,\,\,\,\left( {1374.57 + 687.86} \right):\left( {26.13 + 74.14} \right)\\ = \left( {2.687.57 + 687.86} \right):\left[ {26.13 + 74.\left( {13 + 1} \right)} \right]\\ = \left( {687.114 + 687.86} \right):\left[ {\left( {26.13 + 74.13} \right) + 74} \right]\\ = \left[ {687.\left( {114 + 86} \right)} \right]:\left[ {\left( {26 + 74} \right).13 + 74} \right]\\ = \left[ {687.200} \right]:\left[ {100.13 + 74} \right]\\ = \left[ {687.200} \right]:\left[ {1300 + 74} \right]\\ = 1374.100:1374\\ = 100\end{array}\)c) \(\begin{array}{l}\,\,\,\,\left( {124.237 + 152} \right):\left( {870 + 235.122} \right)\\ = \left[ {124.\left( {235 + 2} \right) + 152} \right]:\left[ {870 + 235.\left( {124 - 2} \right)} \right]\\ = \left[ {124.\left( {235 + 2} \right) + 152} \right]:\left[ {870 + 235.\left( {124 - 2} \right)} \right]\\ = \left( {124.235 + 124.2 + 152} \right):\left( {870 + 235.124 - 235.2} \right)\\ = \left( {124.235 + 248 + 152} \right):\left( {870 + 235.124 - 470} \right)\\ = \left( {124.235 + 400} \right):\left( {400 + 235.124} \right)\\ = 1\end{array}\)d) \(\begin{array}{l}\,\,\,\,\,\left( {500.9 - 250.18} \right):\left( {1 + 2 + 3 +  \ldots  + 2020 + 2021} \right)\\ = \left( {250.2.9 - 250.18} \right):\left( {1 + 2 + 3 +  \ldots  + 2020 + 2021} \right)\\ = \left( {250.2.9 - 250.18} \right):\left( {1 + 2 + 3 +  \ldots  + 2020 + 2021} \right)\\ = \left( {250.2.9 - 250.18} \right):\left( {1 + 2 + 3 +  \ldots  + 2020 + 2021} \right)\\ = \left( {250.18 - 250.18} \right):\left( {1 + 2 + 3 +  \ldots  + 2020 + 2021} \right)\\ = 0:\left( {1 + 2 + 3 +  \ldots  + 2020 + 2021} \right)\\ = 0\end{array}\)