We drop constants and lower-order terms because Big-O tracks growth shape, not exact operation counts. Multiplying by two or adding a fixed setup does not change how a curve bends as input explodes.
Say an algorithm does 3n + 100 steps. For small n the hundred dominates. But as n reaches millions, the 3n swamps it, and the factor three does not change that it grows linearly. So we call it O(n).
This keeps comparisons honest and hardware-free. A constant might just come from one machine being faster. By ignoring it, Big-O captures the property that survives across computers: which algorithm pulls ahead as the problem gets large.
Rewriting in plainer words…
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