Algebraic Expressions

An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. For example, $$3x + 5$$ is an algebraic expression.

A coefficient is a numerical factor that multiplies a variable in an algebraic expression. For example, in $$4x$$ , 4 is the coefficient.

A constant is a fixed value that does not change. For example, in the expression $$2x + 3$$ , the number 3 is a constant.

To evaluate an algebraic expression, substitute the values of the variables into the expression and perform the operations. For example, to evaluate $$3a + 2$$ when $$a = 4$$ , calculate $$3(4) + 2 = 14$$ .

Simplifying an algebraic expression means to combine like terms and reduce it to its simplest form. For example, $$2x + 3x = 5x$$ .

An expression is a combination of numbers, variables, and operations without an equality sign, while an equation states that two expressions are equal, indicated by an equality sign (e.g., $$2x + 3 = 7$$ ).

A variable is a symbol, usually a letter, that represents an unknown value in an expression or equation. For example, in $$x + 5$$ , $$x$$ is a variable.

The order of operations is the sequence in which calculations are performed: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This is often remembered by the acronym PEMDAS.

To translate a verbal expression into an algebraic expression, identify keywords and their mathematical meanings. For example, 'twice a number' translates to $$2n$$ .

Like terms are terms that have the same variable raised to the same power. For example, $$3x$$ and $$5x$$ are like terms, while $$3x$$ and $$4y$$ are not.