Examine The Following Expression: $\[ P^2 - 3 + 3p - 8 + P + P^3 \\]Which Statements About The Expression Are True? Check All That Apply. - The Constants, \[$-3\$\] And \[$-8\$\], Are Like Terms. - The Terms

Feb 27, 2025 by ADMIN 211 views

**Simplifying Algebraic Expressions: An In-Depth Analysis**

Understanding the Basics of Algebraic Expressions

Algebraic expressions are a fundamental concept in mathematics, and they play a crucial role in solving various mathematical problems. An algebraic expression is a combination of variables, constants, and mathematical operations. In this article, we will examine the given expression: $p^2 - 3 + 3p - 8 + p + p^3$ . Our goal is to simplify this expression and determine which statements about it are true.

The Given Expression

The given expression is $p^2 - 3 + 3p - 8 + p + p^3$ . To simplify this expression, we need to combine like terms. Like terms are terms that have the same variable raised to the same power.

Combining Like Terms

To combine like terms, we need to group the terms that have the same variable raised to the same power. In the given expression, we have three terms with the variable $p$ raised to the power of 2, three terms with the variable $p$ raised to the power of 1, and one term with the variable $p$ raised to the power of 3.

p^2 - 3 + 3p - 8 + p + p^3
= (p^2 + p^3) + (3p + p) + (-3 - 8)
= p^2 + p^3 + 4p - 11

Analyzing the Statements

Now that we have simplified the expression, let's analyze the given statements.

The constants, ${-3}$ and ${-8}$ , are like terms. This statement is false. The constants ${-3}$ and ${-8}$ are not like terms because they do not have the same variable raised to the same power.
The terms ${p^2}$ and ${p^3}$ are like terms. This statement is false. The terms ${p^2}$ and ${p^3}$ are not like terms because they have different variables raised to different powers.
The terms ${3p}$ and ${p}$ are like terms. This statement is true. The terms ${3p}$ and ${p}$ are like terms because they have the same variable raised to the same power.
The expression can be simplified by combining like terms. This statement is true. We have already simplified the expression by combining like terms.

Conclusion

In conclusion, the given expression can be simplified by combining like terms. The terms ${3p}$ and ${p}$ are like terms, and the expression can be simplified by combining them. However, the constants ${-3}$ and ${-8}$ are not like terms, and the terms ${p^2}$ and ${p^3}$ are not like terms.

Key Takeaways

Like terms are terms that have the same variable raised to the same power.
To simplify an algebraic expression, we need to combine like terms.
The terms ${3p}$ and ${p}$ are like terms.
The constants ${-3}$ and ${-8}$ are not like terms.
The terms ${p^2}$ and ${p^3}$ are not like terms.