Tháng Ba 29, 2024

Tính nhanh: \(a)\ {{56}^{2}}-{{44}^{2}}-{{23}^{2}}+{{77}^{2}}\) \(b)\ {{103}^{2}}-{{3}^{2}}-100.6\) \(c)\ {{203}^{2}}-{{103}^{2}}\) \(d)\ 20,{{5}^{2}}-10,{{5}^{2}}\)

Tính nhanh:

\(a)\ {{56}^{2}}-{{44}^{2}}-{{23}^{2}}+{{77}^{2}}\)

\(b)\ {{103}^{2}}-{{3}^{2}}-100.6\)

\(c)\ {{203}^{2}}-{{103}^{2}}\)

\(d)\ 20,{{5}^{2}}-10,{{5}^{2}}\)

Lời giải chi tiết:

Hướng dẫn chi tiết:

\(\begin{array}{l}a)\;{56^2} – {44^2} – {23^2} + {77^2}\\ = \left( {{{56}^2} – {{44}^2}} \right) – \left( {{{23}^2} – {{77}^2}} \right)\\ = \left( {56 + 44} \right)\left( {56 – 44} \right) – \left( {23 + 77} \right)\left( {23 – 77} \right)\\ = 100.12 – 100.\left( { – 54} \right)\\ = 100\left( {12 + 54} \right)\\ = 100.66 = 6600\end{array}\)

\(\begin{array}{l}b)\;{103^2} – {3^2} – 100.6\\ = \left( {103 – 3} \right)\left( {103 + 3} \right) – 100.6\\ = 100.106 – 100.6\\ = 100\left( {106 – 6} \right)\\ = 100.100 = 10000\end{array}\)

\(\begin{array}{l}c) \;{203^2} – {103^2}\\ = \left( {203 – 103} \right)\left( {203 + 103} \right)\\ = 100.306 = 30600\end{array}\)

\(\begin{array}{l}d)\;20,{5^2} – 10,{5^2}\\ = \left( {20,5 – 10,5} \right)\left( {20,5 + 10,5} \right)\\ = 10.31 = 310\end{array}\)