Question

How do you write an expression for “the product of $p$ and $q$”?

Answer 1

Hint: First understand the concept of constant, variables, algebraic expression, terms of an algebraic expression, product. Then write an expression for “the product of $p$ and $q$” using the definition of product and algebraic expression.

Complete step by step answer:
In algebra, we use two types of symbols – constants and variables. A symbol which has a fixed value is called a constant.
For example, each of $9, - 5,0,\dfrac{3}{5}, - \dfrac{7}{{11}},3\dfrac{5}{8}$ etc. is a constant.
A symbol which can be given various numerical values is called a variable. Thus, a variable is a number which does not have a fixed value, i.e., it can take different values.
So variables are generalized numbers or unknown numbers. We use the letters $x,y,z,m,n,...$ etc. to denote a variable. Variables are also known as literals (or literal numbers).
Since the variables (literals) are numbers, they obey all the rules of operations of addition, subtraction, multiplication and division of numbers.
Algebraic expression: A collection of constants and variables connected by one or more of the operations of addition, subtraction, multiplication and division is called an algebraic expression.
For example, $4x + 5,9y - 13$ are algebraic expressions
Terms of an algebraic expression: The various parts of an algebraic expression separated by + or – sign are called the terms of the algebraic expression.
Constant term: The term of an algebraic expression having no variables is called its constant term.
Product: When two or more constants or literals (or both) are multiplied, then the result so obtained is called the product.
For example: $3xy$ is the product of $3,x$ and $y$.
Given statement: “the product of $p$ and $q$”
So, $pq$ is the product of $p$ and $q$.

Therefore, the expression for “the product of $p$ and $q$” is $pq$.

Note: Multiplication and division do not separate the terms of an algebraic expression. Thus, $5xy$ is one term. Also, $3{x^2}yz$ is one term, while $5x + y$ has two terms $5x$ and $y$.