Select The Correct Answer.Which Statement Correctly Describes This Expression?$2m^3 - 11$A. The Cube Of Twice A Number Decreased By 11B. Twice The Cube Of A Number Subtracted From 11C. The Difference Of Twice A Number And 11 CubedD. The

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In algebra, expressions are a combination of variables, constants, and mathematical operations. They can be simple or complex, and understanding their structure is crucial for solving equations and inequalities. In this article, we will delve into the expression $2m^3 - 11$ and explore the correct description of its meaning.

What is the Expression $2m^3 - 11$?

The given expression is $2m^3 - 11$. To understand its meaning, let's break it down:

• $2m^3$ represents twice the cube of a number, where $m$ is the variable and $3$ is the exponent.
• The negative sign in front of $11$ indicates that $11$ is being subtracted from the expression.

Analyzing the Options

Now, let's examine the given options to determine which one correctly describes the expression $2m^3 - 11$:

A. The cube of twice a number decreased by 11

This option suggests that the expression represents the cube of twice a number, which is then decreased by $11$. However, this description is not accurate because the expression $2m^3 - 11$ does not involve the cube of twice a number.

B. Twice the cube of a number subtracted from 11

This option implies that the expression represents twice the cube of a number, which is then subtracted from $11$. Although this description is close, it is not entirely accurate because the expression $2m^3 - 11$ does not involve subtracting from $11$.

C. The difference of twice a number and 11 cubed

This option suggests that the expression represents the difference between twice a number and $11$ cubed. However, this description is not accurate because the expression $2m^3 - 11$ does not involve $11$ cubed.

D. The cube of twice a number decreased by 11

This option is the most accurate description of the expression $2m^3 - 11$. It correctly represents the cube of twice a number, which is then decreased by $11$.

Conclusion

In conclusion, the correct description of the expression $2m^3 - 11$ is option D: The cube of twice a number decreased by 11. This expression represents twice the cube of a number, which is then decreased by $11$. Understanding the structure of algebraic expressions is essential for solving equations and inequalities, and this article has provided a closer look at the expression $2m^3 - 11$.

Key Takeaways

• Algebraic expressions are a combination of variables, constants, and mathematical operations.
• Understanding the structure of algebraic expressions is crucial for solving equations and inequalities.
• The expression $2m^3 - 11$ represents twice the cube of a number, which is then decreased by $11$.

Frequently Asked Questions

Q: What is the expression $2m^3 - 11$?

A: The expression $2m^3 - 11$ represents twice the cube of a number, which is then decreased by $11$.

Q: What is the correct description of the expression $2m^3 - 11$?

A: The correct description of the expression $2m^3 - 11$ is option D: The cube of twice a number decreased by 11.

Q: Why is understanding algebraic expressions important?

A: Understanding the structure of algebraic expressions is essential for solving equations and inequalities.

Additional Resources

For further learning, consider the following resources:

• Khan Academy: Algebra
• Mathway: Algebra Solver
• Wolfram Alpha: Algebra Calculator

In our previous article, we explored the expression $2m^3 - 11$ and determined that the correct description of its meaning is option D: The cube of twice a number decreased by 11. In this article, we will delve into more questions and answers related to algebraic expressions.

Q&A Session

Q: What is an algebraic expression?

A: An algebraic expression is a combination of variables, constants, and mathematical operations. It can be simple or complex, and understanding its structure is crucial for solving equations and inequalities.

Q: What are the different types of algebraic expressions?

A: Algebraic expressions can be classified into several types, including:

• Monomials: A monomial is an algebraic expression with one term, such as $2x$ or $5y^2$.
• Binomials: A binomial is an algebraic expression with two terms, such as $x + 3$ or $2y - 4$.
• Polynomials: A polynomial is an algebraic expression with multiple terms, such as $x^2 + 3x - 4$ or $2y^2 - 5y + 1$.
• Rational expressions: A rational expression is an algebraic expression that contains fractions, such as $\frac{x}{y}$ or $\frac{2x + 3}{y - 1}$.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, follow these steps:

1. Combine like terms: Combine any like terms in the expression, such as $2x + 3x$ or $4y - 2y$.
2. Simplify fractions: Simplify any fractions in the expression, such as $\frac{x}{y}$ or $\frac{2x + 3}{y - 1}$.
3. Remove any unnecessary parentheses: Remove any unnecessary parentheses in the expression, such as $(x + 3)$ or $(2y - 4)$.

Q: How do I evaluate an algebraic expression?

A: To evaluate an algebraic expression, follow these steps:

1. Substitute the given values: Substitute the given values into the expression, such as $x = 2$ or $y = 3$.
2. Simplify the expression: Simplify the expression using the given values, such as $2x + 3$ or $2y - 4$.
3. Calculate the final value: Calculate the final value of the expression, such as $2(2) + 3$ or $2(3) - 4$.

Q: What is the order of operations in algebra?

A: The order of operations in algebra is:

1. Parentheses: Evaluate any expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Conclusion

In conclusion, algebraic expressions are a fundamental concept in mathematics, and understanding their structure is crucial for solving equations and inequalities. By following the steps outlined in this article, you will become proficient in simplifying and evaluating algebraic expressions.

Key Takeaways

• Algebraic expressions are a combination of variables, constants, and mathematical operations.
• Understanding the structure of algebraic expressions is essential for solving equations and inequalities.
• The order of operations in algebra is parentheses, exponents, multiplication and division, and addition and subtraction.

Frequently Asked Questions

Q: What is the difference between an algebraic expression and an equation?

A: An algebraic expression is a combination of variables, constants, and mathematical operations, while an equation is a statement that two expressions are equal.

Q: How do I solve an equation with an algebraic expression?

A: To solve an equation with an algebraic expression, follow these steps:

1. Isolate the variable: Isolate the variable on one side of the equation.
2. Simplify the expression: Simplify the expression using the given values.
3. Calculate the final value: Calculate the final value of the expression.

Additional Resources

For further learning, consider the following resources:

• Khan Academy: Algebra
• Mathway: Algebra Solver
• Wolfram Alpha: Algebra Calculator

By following these resources and practicing algebraic expressions, you will become proficient in solving equations and inequalities.