a: \(66^2+66\cdot68+34^2\)
\(=66^2+2\cdot66\cdot34+34^2\)
\(=\left(66+34\right)^2=100^2=10000\)
b: \(215^2-30\cdot215+225\)
\(=215^2-2\cdot215\cdot15+15^2\)
\(=\left(215-15\right)^2=200^2=40000\)
c: \(601^2-401^2\)
\(=\left(601-401\right)\left(601+401\right)\)
\(=200\cdot1002=200400\)
d: \(25^3-15\cdot25^2+3\cdot25\cdot25-5^3\)
\(=25^3-3\cdot25^2\cdot5+3\cdot25\cdot5^2-5^3\)
\(=\left(25-5\right)^3=20^3=8000\)
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