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While I am not positive of the precise definition of advanced algebra, I would assume advanced algebra refers to trigonometry and calculus principles such as derivatives and optimization.
Algebra, on the other hand, simply deals with the finding of one variable
Example: 5x=3x+4
or perhaps sometimes two to three variables. This is possible when given multiple equations.
Example: 5x+3y+2z=7
7x+9y+4z=5
x+3y+6z=4
Algebra is also distinguished by graphing slope and occasionally logarithmic functions.
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