Basic Algebra Terms

Basic algebra terms you need to know:

Constants

A fixed quantity that does not change. For example: 3, –6, π,

Variables

A variable is a symbol that we assign to an unknown value. It is usually represented by letters such as x, y, or t. For example, we might say that l stands for the length of a rectangle and w stands for the width of the rectangle.

We use variables when we need to indicate how objects are related even though we may not know the exact values of the objects. For example, if we want to say that the length of a rectangle is 3 times the length of its width then we can write

l = 3 × w

Coefficients

The coefficient of a variable is the number that is placed in front of a variable.

For example, 3 × w can be written as 3w and 3 is the coefficient.

Coefficient

 

 

Terms

A term can be any of the following:

• a constant: e.g. 3, 10, π,
• the product of a number (coefficient) and a variable: e.g. –3x, 11y,
• the product of two or more variables: e.g. x², xy, 2y², 7xy

Like terms are terms that differ only in their numerical coefficients. For example: 3a, 22a, are like terms.

Expressions

An expression is made up of one or more terms.

For example:

3w + 4xy + 5

Equations

An equation consists of two expressions separated by an equal sign. The expression on one side of the equal sign has the same value as the expression on the other side.

For example:

4 + 6 = 5 × 2

l = 3 × w

3w + 4xy + 5 = 2w + 3

Quadratic Equations

A Quadratic Equation is an equation of the form:

ax² + bx + c = 0, where a, b and c are numbers and a ≠ 0

For example:

x² + 2x + 3 = 0

2x² + 5x – 7 = 0

2x² + 5x = 8     is a quadratic equation because it can be changed to
2x² + 5x – 8 = 0

x² + x = 0     is a quadratic with c = 0

2x² – 7 = 0     is a quadratic with b = 0

2x + 3 = 0     is not a quadratic because a cannot be 0

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