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Algebra is a branch of mathematics concerning the study of structure, relation and quantity.

Together with geometry, analysis, combinatorics, and number theory, algebra is one of the main branches of mathematics. Elementary algebra is often part of the curriculum in secondary education and provides an introduction to the basic ideas of algebra, including effects of adding and multiplying numbers, the concept of variables, definition of polynomials, along with factorization and determining their roots.

Algebra is much broader than elementary algebra and can be generalized. In addition to working directly with numbers, algebra covers working with symbols, variables, and set elements. Addition and multiplication are viewed as general operations, and their precise definitions lead to structures such as groups, rings and fields.

An algebraic expression is an expression that is written using one or more variables.

Examples:

2x       x – 6       3b + 4       p + q

An expression is a combination of numbers, operators, grouping symbols (such as brackets and parentheses) and/or free variables and bound variables arranged in a meaningful way which can be evaluated. Bound variables are assigned values within the expression (they are for internal use) while free variables can take on values from outside the expression.

Simplifying expressions requires a lot of practice. First, you need to have a clear and thorough understanding of the properties of integers and real numbers. Even though these properties may look obvious, it becomes difficult to identify them in given expressions.