Bottom of pan burnt on crud how to clean

Had to change all my -pots and pans due to new ceramic stove top. All my copper bottom pans rocked. Due to high cost of replacement I bought at thrift store farberware, which the bottom of pan is black. Tried bar keepers cleanser, made small improvement, too much scrubbing poor results. Tried hydrogen peroxide and baking soda, didn't work. Any suggestions? Thanks in advance.

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