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Definition of algebraic expression. : an expression obtained by a finite number of the fundamental operations of algebra upon symbols representing numbers.
For example, 3 x 2 â 2 x y + c {\displaystyle 3x^{2}-2xy+c} is an algebraic expression. Since taking the square root is the same as raising to the power 1 2 {\displaystyle {\tfrac {1}{2}}} , is also an algebraic expression. By contrast, transcendental numbers like Ï and e are not algebraic. A rational expression is an expression that may be rewritten to a rational fraction by using the properties of the arithmetic operations (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions).