5) \(892^2+892\cdot216+108^2\)
\(=892^2+2\cdot892\cdot1008+108^2\)
\(=\left(892+108\right)^2\)
\(=1000^2\)
\(=1000000\)
6) \(10,2\cdot9,8-9,8\cdot0,2+10,2^2-10,2\cdot0,2\)
\(=9,8\cdot\left(10,2-0,2\right)+10,2\cdot\left(10,2-0,2\right)\)
\(=9,8\cdot10+10,2\cdot10\)
\(=98+102\)
\(=200\)
7) \(99^3+1+3\cdot\left(99^2+99\right)\)
\(=99^3+3\cdot99^2\cdot1+3\cdot1^2\cdot99+1\)
\(=\left(99+1\right)^3\)
\(=100^3\)
\(=1000000\)
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