** Algebraic Expressions vs Equations **

Algebra is one of the main branches of mathematics and defines some of the fundamental operations contributing to the human understanding of mathematics, such as addition, subtraction, multiplication and division. Algebra also introduces the concept of variables, which allows an unknown quantity to be represented by a single letter, hence the convenience of manipulation in applications.

**More about Algebraic Expressions**

A concept or an idea can be expressed mathematically using the basic tools available in the algebra. Such an expression is known as an algebraic expression. These expressions consist of numbers, variables, and different algebraic operations.

For example consider the statement “to form the mixture, add 5 cups of x and 6 cups of y”. It is reasonable to express the mixture as 5x+6y. We do not know what or how much x and y are, but it gives the relative measures in the mixture. The expression makes sense, but not complete sense mathematically. x/y, x^{2}+y, xy+x^{c} are all examples of expressions.

For ease of use, algebra introduces its own terminology for the expressions.

1. The exponent 2. Coefficients 3. Term 4. Algebraic operator 5. A constant

N.B: a constant can also be used as a coefficient.

Also, when performing algebraic operations (e.g. when simplifying an expression), the operator precedence has to be followed. Operator precedence (priority) in descending order is as follows;

*Brackets*

*Of*

*Division*

*Multiplication*

*Addition*

*Subtraction*

This order is commonly known by the mnemonic formed by the first letters of each operation, which is BODMAS.

Historically the algebraic expression and operations brought a revolution in mathematics because the formulation of mathematical concepts was easier, so is the following derivations or conclusions. Prior to this form, the problems were mostly solved using ratios.

**More about Algebraic Equation**

An algebraic equation is formed by connecting two expressions using an assignment operator denoting the equality of the two sides. It gives that the left hand side is equal to the right hand side. For example, x^{2}-2x+1=0 and x/y-4=3x^{2}+y are algebraic equations.

Usually the equality conditions are satisfied only for certain values of the variables. These values are known as the solutions of the equation. When substituted, these values exhaust the expressions.

If an equation consists of polynomials on both sides, the equation is known as a polynomial equation. Also, if only one variable is in the equation, it is known as a univariate equation. For two or more variables, the equation is called multivariate equations.

**What is the difference between Algebraic Expressions and Equations?**

• Algebraic expression is a combination of variables, constants and operators such that they form a term or more to give a partial sense of relations between each variable. But the variables can assume any value available in its domain.

• An equation is two or more expressions with an equality condition and the equation is true for one or several values of the variables. An equation makes complete sense as long as the equality condition is not violated.

• An expression can be evaluate for given values.

• An equation can be solved to find an unknown quantity or variable, owing to the above fact. The values are known as the solution to the equation.

• Equation carries an equal sign (=) in the equation.