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In mathematics, an algebraic expression is an expression built up from constants (usually, algebraic numbers) variables, and the basic algebraic operations: addition (+), subtraction (-), multiplication (×), division (÷), whole number powers, and roots (fractional powers).
In the equation 7x − 5 = 2, the sides of the equation are expressions. In mathematics, an expression is a written arrangement of symbols following the context-dependent, syntactic conventions of mathematical notation. Symbols can denote numbers, variables, operations, and functions. [1]
In general, the expression "a − b − c" can be defined to mean either (a − b) − c or a − (b − c), but these two possibilities lead to different answers. To resolve this issue, one must establish an order of operations, with different orders yielding different results.
They may also be performed, in a similar way, on variables, algebraic expressions, [2] and more generally, on elements of algebraic structures, such as groups and fields. [3] An algebraic operation may also be defined more generally as a function from a Cartesian power of a given set to the same set.
The acronym's procedural application does not match experts' intuitive understanding of mathematical notation: mathematical notation indicates groupings in ways other than parentheses or brackets and a mathematical expression is a tree-like hierarchy rather than a linearly "ordered" structure; furthermore, there is no single order by which ...
The expression on the right side of the "=" sign is the right side of the equation and the expression on the left of the "=" is the left side of the equation. For example, in + = + x + 5 is the left-hand side (LHS) and y + 8 is the right-hand side (RHS).