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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.
An expression like 1/2x is interpreted as 1/(2x) by TI-82, [3] as well as many modern Casio calculators [36] (configurable on some like the fx-9750GIII), but as (1/2)x by TI-83 and every other TI calculator released since 1996, [37] [3] as well as by all Hewlett-Packard calculators with algebraic notation.
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). [43] For example, 3x 2 − 2xy + c is an algebraic expression.
The calculator can evaluate and simplify algebraic expressions symbolically. For example, entering x^2-4x+4 returns x 2 − 4 x + 4 {\displaystyle x^{2}-4x+4} . The answer is " prettyprinted " by default; that is, displayed as it would be written by hand (e.g. the aforementioned x 2 − 4 x + 4 {\displaystyle x^{2}-4x+4} rather than x^2-4x+4 ).
In calculus and mathematical analysis, algebraic operation is also used for the operations that may be defined by purely algebraic methods. For example, exponentiation with an integer or rational exponent is an algebraic operation, but not the general exponentiation with a real or complex exponent. Also, the derivative is an operation that is ...
Some graphing calculators have a computer algebra system (CAS), which means that they are capable of producing symbolic results. These calculators can manipulate algebraic expressions, performing operations such as factor, expand, and simplify. In addition, they can give answers in exact form without numerical approximations. [6]
Algebraic notation describes the rules and conventions for writing mathematical expressions, as well as the terminology used for talking about parts of expressions. For example, the expression + has the following components: Algebraic expression notation: 1 – power (exponent) 2 – coefficient 3 – term