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2. Difference of two squares - Wikipedia

   en.wikipedia.org/wiki/Difference_of_two_squares

   The resulting identity is one of the most commonly used in mathematics. Among many uses, it gives a simple proof of the AM–GM inequality in two variables. The proof holds in any commutative ring. Conversely, if this identity holds in a ring R for all pairs of elements a and b, then R is commutative. To see this, apply the distributive law to ...

3. Elementary algebra - Wikipedia

   en.wikipedia.org/wiki/Elementary_algebra

   They may also be performed, in a similar way, on variables, algebraic expressions, [6] and more generally, on elements of algebraic structures, such as groups and fields. [7] 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. Expression (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Expression_(mathematics)

   Expressions are often contrasted with statements—syntactic entities that have no value (an instruction). Representation of the expression (8 − 6) × (3 + 1) as a Lisp tree, from a 1985 Master's Thesis [46] Except for numbers and variables, every mathematical expression may be viewed as the symbol of an operator followed by a sequence of ...

5. Algebra - Wikipedia

   en.wikipedia.org/wiki/Algebra

   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.

6. Algebraic expression - Wikipedia

   en.wikipedia.org/wiki/Algebraic_expression

   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).

7. Cross-multiplication - Wikipedia

   en.wikipedia.org/wiki/Cross-multiplication

   In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable.