Problem 24 Combine like terms. $$9 z^{2}+... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

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Chapter 10: Problem 24

Combine like terms. $$9 z^{2}+11 z^{2}-8 z^{2}$$

Short Answer

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12z^2

Step by step solution

Identify Like Terms

Look at each term in the expression. All terms are like terms because they all contain the variable with the same exponent, which is 2. The terms are: $9z^2$, $11z^2$, and $-8z^2$.

Add the Coefficients

To combine the like terms, add the coefficients of the like terms together. The coefficients are 9, 11, and -8. So, calculate: $9 + 11 - 8$.

Simplify the Sum

Simplify the sum of the coefficients calculated in the previous step: $9 + 11 - 8 = 12$.

Form the Final Expression

Attach the variable with its exponent to the resulting coefficient: $12z^2$.

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Key Concepts

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

Like Terms

Understanding like terms is essential for simplifying algebraic expressions. Like terms are terms that have the exact same variables raised to the same powers. In the given expression $9z^2, 11z^2, -8z^2$, all terms are like terms because they contain the variable $z$ with the same exponent of 2. This shared characteristic allows us to combine them efficiently.
One important property of like terms is that you can combine them by performing arithmetic operations on their coefficients. Identifying like terms correctly is the first crucial step before simplification.

Coefficients

Coefficients are numerical factors that multiply the variables in an algebraic expression. In our example, the coefficients of the terms $9z^2, 11z^2, -8z^2$ are 9, 11, and -8, respectively.
The key task is to combine these coefficients to simplify the expression. In simpler terms, it's like adding or subtracting the numerical parts, while ignoring the variable part temporarily.
The process of combining like terms often involves adding coefficients. Be mindful of the signs: positive and negative coefficients can affect the outcome of your sum.

Simplification

Simplification is the process of reducing an algebraic expression to its simplest form. After identifying like terms and their coefficients, you perform the necessary arithmetic operations to combine these coefficients.
In the given problem, we added the coefficients as follows: $9 + 11 - 8 = 12$.
The final step is to reattach the variable part to the combined coefficient, resulting in the simplified term $12z^2$. This step ensures that the expression is easier to read and work with in further mathematical operations.

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91影视

Combine like terms. $$9 z^{2}+11 z^{2}-8 z^{2}$$

Short Answer

Step by step solution

Identify Like Terms

Add the Coefficients

Simplify the Sum

Form the Final Expression

Key Concepts

Like Terms

Coefficients

Simplification

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