Problem 4 \(8 p^{2}+9 w^{3}+2 p^{2}+13 w^{... [FREE SOLUTION]

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Elementary Algebra

Laura Bracken, Ed Miller

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1 Edition

Chapter 5: Problem 4

$8 p^{2}+9 w^{3}+2 p^{2}+13 w^{3}$

Short Answer

Expert verified

The simplified expression is \10p^2 + 22w^3.\

Step by step solution

- Identify Like Terms

Look at the given expression and identify the like terms. Like terms are terms that have the same variable raised to the same power. In this case, the like terms are $8p^2$ and $2p^2$, and the like terms $9w^3$ and $13w^3$.

- Combine Like Terms with $p^2$

Add the coefficients of the like terms with $p^2$ together. \[8p^2 + 2p^2 = (8 + 2)p^2 = 10p^2.\]

- Combine Like Terms with \)w^3\)

Add the coefficients of the like terms with $w^3$ together. \[9w^3 + 13w^3 = (9 + 13)w^3 = 22w^3.\]

- Write the Final Combined Expression

Combine the results from Step 2 and Step 3 to write the final expression: \[10p^2 + 22w^3.\]

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Key Concepts

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

like terms

In algebra, like terms are terms that have the same variable raised to the same power.
They can be combined by adding or subtracting their coefficients.
For example, in the expression $8p^2 + 9w^3 + 2p^2 + 13w^3$, the like terms are $8p^2$ and $2p^2$, as well as $9w^3$ and $13w^3$.
It's important to identify like terms because combining them simplifies the expression.
This makes further calculations easier.

algebraic expressions

An algebraic expression is a combination of variables, numbers, and at least one arithmetic operation (addition, subtraction, multiplication, or division).
In the given exercise, $8p^2 + 9w^3 + 2p^2 + 13w^3$ is an algebraic expression.
Expressions like these are fundamental in algebra because they help model real-world situations, solve problems, and perform computations.
Understanding how to manipulate algebraic expressions by combining like terms is a crucial skill.

coefficients

A coefficient is a number that is multiplied by a variable in an algebraic expression.
For instance, in $8p^2$, the coefficient is 8.
Similarly, in $9w^3$, the coefficient is 9.
When we combine like terms, we add or subtract these coefficients.
In our exercise, you first identify like terms and then add their coefficients:
\[8p^2 + 2p^2 = (8 + 2)p^2 = 10p^2\]
Similarly for $w^3$ terms:
\[9w^3 + 13w^3 = (9 + 13)w^3 = 22w^3\]

polynomial addition

Polynomial addition involves combining like terms in a polynomial.
This simplifies the expression for easier handling.
In our provided exercise, the expression $8p^2 + 9w^3 + 2p^2 + 13w^3$ is simplified by adding the coefficients of like terms:
First, we add the like terms with $p^2$:
\[8p^2 + 2p^2 = 10p^2\]
Then, we add the like terms with $w^3$:
\[9w^3 + 13w^3 = 22w^3\]
The final simplified expression is:
$10p^2 + 22w^3$
This process helps in solving and understanding larger and more complex polynomials in algebra.

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91影视

\(8 p^{2}+9 w^{3}+2 p^{2}+13 w^{3}\)

Short Answer

Step by step solution

- Identify Like Terms

- Combine Like Terms with \(p^2\)

- Combine Like Terms with \)w^3\)

- Write the Final Combined Expression

Key Concepts

like terms

algebraic expressions

coefficients

polynomial addition

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