Algebra

Method of Indeterminate Coefficients

If 𝐴+𝐵𝑥+𝐶𝑥²+⋯=𝐴'+𝐵'𝑥+𝐶'𝑥²+⋯ be an equation which holds for all values of 𝑥, the coefficients 𝐴, 𝐵, ⋯ not involving 𝑥, then 𝐴=𝐴', 𝐵=𝐵', 𝐶=𝐶', ⋯; that is, the coefficients of like powers of 𝑥 must be equal. Proved by putting 𝑥=0, and dividing by 𝑥 alternately. See (234) for an example. 232

Sources and References

https://archive.org/details/synopsis-of-elementary-results-in-pure-and-applied-mathematics-pdfdrive