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Chapter 1: Problem 81

List the factors in each expression. $$ s t $$

Short Answer

Expert verified
The factors are 's' and 't'.

Step by step solution

01

Identify the Terms in the Expression

The given expression is a product of variables. Identify the individual variables or terms in the expression. Here, the terms are 's' and 't'.
02

List the Factors

Factors in an expression are the components that are multiplied together. Since 's' and 't' are multiplied together in the expression, the factors are 's' and 't'.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Variables
Variables are symbols used to represent unknown values or quantities in an expression. Typically, they are denoted by letters such as 's', 't', 'x', 'y', and 'z'. Variables can vary and take on different values depending on the equation or context.
They are foundational in algebra because they allow us to generalize mathematical statements and solve equations for unknowns.
For example, in the expression provided, 's' and 't' are both variables. They could potentially represent any number, but we treat them as placeholders until we have more information or need to solve for them.

Some key points to remember about variables:
  • Variables can represent any value.
  • They are used to simplify and generalize mathematical expressions.
  • Variables are flexible and can change to suit different conditions or problems.
Identifying Terms in an Expression
Terms in an expression are the parts separated by addition or subtraction signs. Each term consists of numbers, variables, or a combination of both.
In the expression given in the exercise, we have multiplication of variables 's' and 't'. Though it appears simple, it can be broken down into its factors.

Here鈥檚 how we identify terms:
  • Look for all the parts of the expression that are combined through addition or subtraction. Each part is a term.
  • In our case, since we only have multiplication and no addition or subtraction, 's' and 't' are treated as a single term (the product 's t').
  • Remember that multiplication does not change the number of terms in this context鈥攊t just combines them into a single product.

By understanding terms, we simplify algebraic expressions and make them easier to work with and break down.
The Multiplication of Variables
When we multiply variables, we are combining them into a single product. This process is straightforward but foundational for more complex algebra.
For instance, in the given expression 's t', 's' and 't' are multiplied together. Here's what you need to know about multiplying variables:
  • Each variable acts as a separate factor within the product.
  • The product of two variables is simply their multiplication without any additional symbols (like dot or asterisk).
  • If we were to multiply 's' and 't' again, it would be expressed as 's t t' or \(s t^2\) if 't' is repeated.

Simplifying multiplication of variables helps in factorizing and solving algebraic expressions efficiently. By recognizing each variable as a factor, we can reconstruct or deconstruct expressions effortlessly.

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Most popular questions from this chapter

Simplify. \(5 t-\\{7 t-[4 r-3(t-7)]+6 r\\}-4 r\)

Evaluate using a calculator. $$ (t+4)^{2}-12 \div(19-17)+68, \text { for } t=5 $$

Simplify using a calculator. Round your answer to the nearest thousandth. $$ \frac{46-(3-8)^{3}}{2\left[35-(18-26)^{2}\right]} $$

Simplify. $$ 12 a^{2}-3 a b+5 b^{2}-5\left(-5 a^{2}+4 a b-6 b^{2}\right) $$

If \(n>0, m>0,\) and \(n \neq m,\) classify each of the following as either true or false. $$ m-n=-(n-m) $$
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