A variable is a symbol that is used to represent an unknown quantity. For example, x, y, z.
If x and y are variables, then the product xy is also a variable.
A term can be: a single number. For example, 2, 5. a variable, or a product of variables (which may be raised to powers). For example, z, b3, [pic]. a product of a number and one or more variables (which may be raised to powers). For example, 3x, – 4yz, 7a2 b3 .
In a term that is the product of a number and one or more variables, the number is called the numerical coefficient or simply the coefficient. For example, in the term –2b3, the coefficient is –2 and the variable part is b3.
Like and unlike algebraic terms
Like algebraic terms are defined as those terms which are represented by the same algebraic symbol, regardless of the sign or the magnitude of their coefficients.
Thus 5x, –3x, [pic] and [pic] are like algebraic terms since they are all represented by the same symbol x.
Similarly 3a2 , –2a2, 0.4a2 and [pic]a2 are like terms.
Unlike algebraic terms are terms that are represented by different algebraic symbols.
Thus 7b, 3b2 and –2b3 are all unlike terms even though they are powers of the same variable, b.
Similarly, [pic], [pic]and [pic], read as “y one”, “y two” and “y three” respectively, are unlike algebraic terms and are interpreted as the “first y”, the “second y” and the “third y” .
When we combine numbers and variables with the ordinary operations of arithmetic (in some meaningful way), the result is called an algebraic expression. Addition/subtraction signs separate algebraic expressions into terms.
(1) 2 + 3x – 4y + 5z, (2) 7a2 b3 + 5, (3) (x – y)(y – z)(z – x), (4) [pic].
The expressions above have no specific value unless we assign values to the variables a, b, x, y, and z. The values of these expressions may vary depending on the values assigned to these symbols.
Ex. Find the value of