Defining Expression, Equation and Terms.
Expressions in algebra are distinct because they do not have an equal sign. But equations contain the equal sign linking the left and the right hand sides of the equation. Terms are the parts associated with either an expression or equation that are composed of variables, constants and coefficients.
Let’s consider an example.
3x + 9b – 5 – is an example of an expression, and the terms are, 3x, 9b and 5.
12xy – 6pq = 13 – is an example of an expression and the terms are 12xy, 6pq and 13.
As we can observe, the terms are made of variables that are letters like x, y, p, q and so on. Variables are also linked with a value known as a coefficient. We can also observe numbers in both the expression and equation that are known as constants.
Difference between Constants and Variables
A major difference between constants and variables is that the value of a constant remains the same, but the value of a variable keeps changing. Constants are written as numbers but variables as mentioned earlier are written as letters or as symbols.
Rapid Recall
What is the difference between constants and variables? | |
Constant | Variables |
A constant does not change its value as the equation is solved. | A variable, on the other hand, changes its value depending on the equation. |
Constants are usually written in numbers(whether fractions, integers, decimals or real numbers). | Variables are written as letters or symbols. |
Constants usually represent the known values in an equation or expression. | Variables, on the other hand, represent unknown values. |
Constants have fixed face values. | Variables do not have a fixed face value. |
Solved Examples
Example 1:
Identify the constants and variables in the following options:
- \(7x + 4y + 3z + 15 = 0\)
- \(2f^{3} – 14 – 3f = 6x\)
- \(8m^{2} – 16 + 4m(2n) + 13\)
- \(3cd – 2uv – 19 + x = 19\)
- \(15x^{3} – xy^{2} + 31 = 23\)
Solution:
- \(7x + 4y + 3z + 15 = 0\)
Variables: 7x, 4y, 3z
Constant: 15
2. \(2f^{3} – 14 – 3f = 6x\)
Variables: \(2f^{3}, 3f, 6x\)
Constant: 14
3. \(8m^{2} – 16 + 4m(2n) + 13\)
Variables: \(8m^{2}, 4m, 2n\)
Constants: 16, 13
4. \(3cd – 2uv – 19 + x = 19\)
Variables: 3cd, 2uv, x
Constant: 19
5. \(15x^{3} – xy^{2} + 31 = 23\)
Variables: \(15x^{2}, \text{ }xy^{2}\)
Constants: 31, 23
The creation of algebra is attributed to a Persian mathematician who mentioned algebraic strategies in his book written in 830 AD.
Numbers are always used as constants in algebraic expressions and equations and cannot be used as variables. This is because the value of the number is already known, but the value of a variable changes as the expression or equation is solved.
Every algebraic equation has a solution, especially the value of the variables, and this solution when substituted in the equation balances the right and left sides of the equation.