## Variables and Algebraic Expression

5.1  Variables and Algebraic Expression

Variable:

 Definition 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.

 Example 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:

 Definition 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.

 Example 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.

 Example 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.

 Examples In the term $$–8xy^2$$, state the coefficient of: (i) $$-x$$ (ii) $$xy^2$$ (i) $$-8xy^2=8y^2\times(-x)$$ The coefficient of $$-x$$ is $$8y^2$$. (ii) $$-8xy^2=(-8)\times xy^2$$ The coefficient of $$xy^2$$ is $$-8$$.

Like terms:

 Definition Contain the same variables with the same power.

• Example: $$4k$$ and $$\dfrac{1}{12}k$$

Unlike terms:

 Definition Contain different variables or the same variables with different powers.

 Examples (i) $$2x$$ and $$9m$$ Variables $$x$$ and $$m$$ are different. (ii) $$x$$ and $$6x^2$$ The powers of the variable $$x$$ are different.