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Chapter 1: Problem 44

Combine like terms. $$ s^{4} t-5 s^{4} t $$

Short Answer

Expert verified
-4 s^{4} t

Step by step solution

01

Identify Like Terms

Observe the given expression: oindent \(s^{4} t - 5 s^{4} t\) Both terms have the same variables with the same exponents, so they are like terms.
02

Combine the Coefficients

Combine the coefficients of the like terms. Since the coefficients are 1 and -5, we get: \(1 - 5 = -4\)
03

Write the Combined Term

Multiply the combined coefficient with the common variables: \(-4 \times s^{4} t\). Thus, the simplified form is: \(-4 s^{4} t\).

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Key Concepts

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

like terms
When working with algebraic expressions, identifying like terms is a crucial step. Like terms are terms that have the exact same variables raised to the same power. For example, in the expression \(s^{4} t - 5 s^{4} t\), both terms have \(s^4t\) as their variables with the same exponents. This makes them like terms. Combining like terms helps simplify expressions by merging terms that share the same variable component.
coefficients
Coefficients are the numerical parts of terms in an algebraic expression. They are the multipliers of the variable parts. For instance, in the term \(5 s^{4} t\), the coefficient is 5. In our given expression, \(s^{4} t - 5 s^{4} t\), the coefficients are 1 and -5 respectively. To combine like terms, you add or subtract their coefficients. Here, you calculate \(1 - 5 = -4\), and then reattach this result to the common variable part, which results in \(-4 s^{4} t\).
simplifying expressions
Simplifying expressions often involves combining like terms and reducing the expression to its simplest form. Starting with \(s^{4} t - 5 s^{4} t\), you first identify like terms. Both terms have the same variable part \(s^4t\). You then combine the coefficients, giving you \(-4 s^{4} t\). Each step makes the expression easier to understand and work with in future calculations.

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