Algebra is built on the idea of using symbols to represent unknown or changeable quantities. A variable is a symbol, usually a letter such as \(x\) or \(y\), that stands in for a value we may not yet know or that may vary depending on context. When a variable is combined with constants (fixed numbers) and operations like addition, subtraction, multiplication, or division, the result is an algebraic expression. For example, \(3x + 5\) is an algebraic expression because it combines the variable \(x\), the constant \(5\), and the operations of multiplication and addition, all without an equals sign.
Within any expression, each term has its own structure. The numerical factor multiplied by a variable in a term is called a coefficient; in the term \(7x\), the coefficient is \(7\). A constant, on the other hand, is a number standing on its own whose value does not change; in \(2x + 9\), the constant is \(9\). To evaluate an expression means to substitute specific numerical values for each variable and then simplify using the order of operations to obtain a single numerical answer.
Two terms are called like terms when they contain the same variable raised to the same power, such as \(3x^2\) and \(-5x^2\). Like terms can be combined by adding or subtracting their coefficients. The distributive property, which states that \(a(b + c) = ab + ac\), is another essential tool: it lets you multiply a single term by every term inside a set of parentheses. For instance, to simplify \(4(2x - 3) + 5x\), you first distribute to get \(8x - 12 + 5x\), and then combine the like terms \(8x\) and \(5x\) to obtain \(13x - 12\).