Variables and Algebraic Expression

5.1  Variables and Algebraic Expression

A quantity whose value is unknown and not fixed, which can represent any value.

  • Letters can be used to represent variables.
  • A variable has a fixed value if the represented quantity is always constant at any time.
  • A variable has a varied value if the represented quantity changes over time.

The travelling time taken by Sofea from her house to the school every day.

\(k\) represents the travelling time taken by Sofea from her house to the school every day.

\(k\) has a varied value because the travelling time of Sofea changes every day.

Algebraic expression:

An expression that combines a number, variable or other mathematical entity with an operation.

  • Examples: \(k,\, y+2,\, \dfrac{z}{3},\, 12rst\)
Determine the values of algebraic expressions:
  • The value of an algebraic expression can be determined by substituting the variables with the given values.

Given that \(x = 3 \) and \(y = 2\).

Calculate the value of \(8x – 5y + 7\).

\(\begin{aligned} &\space8x – 5y + 7 \\\\&= 8(3) – 5(2) + 7 \\\\&=24-10+7 \\\\&=21. \end{aligned}\)

The terms and the coefficients in an expression:
  • Term is every quantity in an expression involving a \(+\) or \(-\) sign.
  • In an algebraic expression, a number is also considered as a term.
  • Algebraic term is a term that contains one variable.

State the terms in \(2pq-7y-3\).

Algebraic terms: \(2pq,\,7y\) and \(3\)

\(2pq\) is the product of the number \(2\) and the variables \(p\) and \(q\).

Meanwhile, \(7y\)  is the product of the number \(7\) and the variable \(y\).

  • The algebraic term that consists of one variable with the power \(1\) is called a linear algebraic term.
  • Coefficient is the factors in a product.

In the term \( –8xy^2\), state the coefficient of:

(i) \(-x\)

(ii) \(xy^2\)


\(-8xy^2=8y^2\times(-x) \)

The coefficient of \(-x\) is \(8y^2\).


\(-8xy^2=(-8)\times xy^2 \)

The coefficient of \(xy^2\) is \(-8\).

Like terms:

Contain the same variables with the same power.

  • Example: \(4k\) and \(\dfrac{1}{12}k\)
Unlike terms:

Contain different variables or the same variables with different powers.


(i) \(2x\) and \(9m\)

Variables \(x\) and \(m\) are different.

(ii) \(x\) and \(6x^2\)

The powers of the variable \(x\) are different.