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An algebraic equation is an equation involving polynomials, for which algebraic expressions may be solutions. If you restrict your set of constants to be numbers, any algebraic expression can be called an arithmetic expression. However, algebraic expressions can be used on more abstract objects such as in Abstract algebra.
Algebraic expressions may be evaluated and simplified, based on the basic properties of arithmetic operations (addition, subtraction, multiplication, division and exponentiation). For example, For example,
An algebraic operation may also be defined more generally as a function from a Cartesian power of a given set to the same set. [4] The term algebraic operation may also be used for operations that may be defined by compounding basic algebraic operations, such as the dot product.
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.
An algebraic expression is an expression built up from algebraic constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by a rational number). [41] For example, 3x 2 − 2xy + c is an algebraic expression.
An algebraic equation is an equation involving only algebraic expressions in the unknowns. ... Vector space – basic algebraic structure of linear algebra;
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