Problem 13 Simplify: \(-3 z^{2}+4 z-8 z^{2}... [FREE SOLUTION]

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Elementary Algebra

David Arnold

$Math Studyset 91影视 Explanations$ Math

2020 Edition

Chapter 1: Problem 13

Simplify: $-3 z^{2}+4 z-8 z^{2}-9 z$.

Short Answer

Expert verified

-11z^{2} - 5z

Step by step solution

Combine Like Terms

First, let's identify and combine the like terms in the expression $-3z^{2} + 4z - 8z^{2} - 9z$. The terms $-3z^{2}$ and $-8z^{2}$ are both $z^{2}$ terms, and the terms $4z$ and $-9z$ are both $z'$ terms. So, we combine them separately:$-3z^{2} - 8z^{2}$ gives $-11z^{2}$ and $4z - 9z$ gives $-5z$. This simplifies our expression to $-11z^{2} - 5z$.

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Key Concepts

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

Combining Like Terms

In algebraic expressions, the concept of combining like terms is crucial for simplification. Like terms are terms that have the same variables raised to the same power. In our example, consider the expression $-3z^{2} + 4z - 8z^{2} - 9z$. Here, $-3z^{2}$ and $-8z^{2}$ are like terms because they both involve $z^{2}$.Similarly, $4z$ and $-9z$ are like terms as they both contain $z$. To combine like terms, you simply add or subtract their coefficients:

For the $z^{2}$ terms: $-3 - 8 = -11$, resulting in $-11z^{2}$.
For the $z$ terms: $4 - 9 = -5$, resulting in $-5z$.

By combining these, we simplify the expression to $-11z^{2} - 5z$. Breaking down the problems in this way helps clarify the process.

Polynomials

Polynomials are expressions made up of terms, which can be constants, variables, or a combination of both raised to various powers. Each term is separated by a plus (+) or minus (-) sign. In our exercise, the expression $-3z^{2} + 4z - 8z^{2} - 9z$ is a polynomial consisting of four terms.Polynomials can have terms with different degrees, where the degree is determined by the highest power of the variable in the term:

The term $-3z^{2}$ has a degree of 2 because the variable $z$ is raised to the second power.
The term $4z$ has a degree of 1, as does $-9z$.

When working with polynomials, simplifying expressions by combining like terms, as we did, is essential for further calculations and problem-solving.

Simplification in Algebra

Simplification in algebra involves reducing an expression to its simplest form. This process often includes combining like terms, factoring, or applying arithmetic operations. The purpose is to make expressions easier to understand and work with in further problem-solving.In the given exercise, we simplified the expression $-3z^{2} + 4z - 8z^{2} - 9z$ by:

Identifying and grouping like terms, i.e., terms with the same variable and exponent.
Combining their coefficients to create a simplified version: $-11z^{2} - 5z$.

Simplification does not change the value of the expression; it merely presents it in a more reduced form, making calculations more straightforward and preventing errors in more complex algebraic operations.

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91影视

Simplify: \(-3 z^{2}+4 z-8 z^{2}-9 z\).

Short Answer

Step by step solution

Combine Like Terms

Key Concepts

Combining Like Terms

Polynomials

Simplification in Algebra

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