Question

Combine like terms. See Example 3. $$ 5 z^{4}+3 z^{4} $$

   Combine like terms. See Example 3.
$$
5 z^{4}+3 z^{4}
$$

Intermediate Algebra

Intermediate Algebra

John Hornsby; Terry… 13th Edition

Chapter 4, Problem 37

Instant Answer

Solved by Expert Rahul Mittal

02/10/2022

Step 1

In this case, $5z^{4}$ and $3z^{4}$ are like terms because they have the same variable and exponent. Show more…

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Combine like terms. See Example 3. $$ 5 z^{4}+3 z^{4} $$

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Key Concepts

Like Terms

Like terms in algebra are terms that have the exact same variable components raised to the same power. Recognizing like terms is crucial because only these can be combined through addition or subtraction, simplifying the expression without altering its overall value.

Coefficient Addition

When combining like terms, the process involves adding or subtracting the numerical coefficients of the terms. The variable part remains unchanged, allowing for a simpler expression that reflects the combined value of the coefficients.

Simplifying Expressions

Simplifying expressions by combining like terms is a fundamental technique in algebra. It reduces the complexity of an expression, making it easier to solve equations and perform further algebraic operations.

Exponents

In expressions involving variables, the exponent indicates the power to which the variable is raised. When combining like terms, the exponents must be the same for the terms to be considered like terms; the common exponent is preserved during the combination process.

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