Problem 43 Combine like terms. $$ -k z^... [FREE SOLUTION]

Chapter 1: Problem 43

Combine like terms. $$ -k z^{6}-k z^{6} $$

Short Answer

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-2k z^{6}

Step by step solution

Identify like terms

Examine the expression $$-k z^{6} - k z^{6} $$ and identify terms that can be combined. Both terms $$-k z^{6} $$ are like terms because they have the same variable raised to the same power.

Add coefficients

Combine the coefficients of the like terms. Since both terms are $$-k z^{6} $$, the coefficients are -k and -k. Therefore, add these coefficients: $$-k + -k = -2k.$$

Write the simplified expression

Combine the result from Step 2 with the common variable term: $$-2k z^{6}.$$

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Key Concepts

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

algebra

In algebra, you work with variables, numbers, and different operations to solve problems. One of the key features is simplifying expressions by combining like terms. Like terms are terms that have the same variable raised to the same power. For instance, in the expression $ -k z^{6} - k z^{6} $, both terms include $ z^{6} $ as the variable term. The goal is to simplify such expressions to their simplest form. This is done by adding or subtracting the coefficients (the numerical part) of these like terms.

polynomial expressions

Polynomial expressions consist of multiple terms summed together, where each term is made up of a constant multiplied by a variable raised to a non-negative integer power. In our example, $ -k z^{6} - k z^{6} $, each term is part of a polynomial expression. To simplify polynomial expressions, you should:

Identify like terms.
Add or subtract their coefficients while retaining the common variable part.

Combining like terms helps in reducing the polynomial to a simpler form, making it easier to understand and solve.

coefficients

Coefficients are the numerical or constant factors that multiply the variable in an algebraic term. For example, in the term $ -k z^{6} $, $ -k $ is the coefficient. When combining like terms, focus on the coefficients, as these are the parts you add or subtract. In step 2 of the solution, the coefficients $ -k $ and $ -k $ are added: $ -k + -k = -2k $. The variable part $ z^{6} $ remains unchanged, resulting in a simplified expression: $ -2k z^{6} $. Understanding how to manipulate coefficients is crucial for mastering algebra and polynomial expressions.

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91影视

Combine like terms. $$ -k z^{6}-k z^{6} $$

Short Answer

Step by step solution

Identify like terms

Add coefficients

Write the simplified expression

Key Concepts

algebra

polynomial expressions

coefficients

One App. One Place for Learning.

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