Simplify The Expression.${ 2x(-11x - 7) }$A. { -22x^2 - 14x$}$B. { -11x^2 - 14x$}$C. { -22x - 14x^2$}$D. ${ 22x^2 - 14x^2\$}

Understanding the Problem

The given problem requires us to simplify the expression $2x(-11x - 7)$. This involves using the distributive property to expand the expression and then combining like terms.

The Distributive Property

The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses. In this case, we have the expression $2x(-11x - 7)$, where $2x$ is the term outside the parentheses and $(-11x - 7)$ is the term inside the parentheses.

Applying the Distributive Property

To simplify the expression, we need to apply the distributive property by multiplying each term inside the parentheses with the term outside the parentheses. This gives us:

$2x(-11x - 7) = 2x(-11x) + 2x(-7)$

Simplifying the Expression

Now that we have applied the distributive property, we can simplify the expression by combining like terms. The expression $2x(-11x) + 2x(-7)$ can be simplified as follows:

$2x(-11x) + 2x(-7) = -22x^2 - 14x$

Comparing the Options

Now that we have simplified the expression, we can compare it with the given options to determine the correct answer.

Option A: $-22x^2 - 14x$

This option matches the simplified expression we obtained earlier.

Option B: $-11x^2 - 14x$

This option is incorrect because it does not match the simplified expression we obtained earlier.

Option C: $-22x - 14x^2$

This option is incorrect because it does not match the simplified expression we obtained earlier.

Option D: $22x^2 - 14x^2$

This option is incorrect because it does not match the simplified expression we obtained earlier.

Conclusion

In conclusion, the correct answer is Option A: $-22x^2 - 14x$. This is because it matches the simplified expression we obtained earlier.

Key Takeaways

• The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses.
• To simplify an expression, we need to apply the distributive property and then combine like terms.
• The correct answer is Option A: $-22x^2 - 14x$.

Additional Resources

For more information on simplifying expressions and applying the distributive property, please refer to the following resources:

• Algebra Tutorial
• Distributive Property
• Simplifying Expressions

Practice Problems

To practice simplifying expressions and applying the distributive property, please try the following problems:

• Simplify the expression $3x(2x + 5)$.
• Simplify the expression $4x(-2x + 3)$.
• Simplify the expression $2x(3x - 2)$.

Answer Key

• $6x^2 + 15x$
• $-8x^2 + 12x$
• $6x^2 - 4x$
  Simplify the Expression: Q&A =============================

Frequently Asked Questions

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses.

Q: How do I apply the distributive property?

A: To apply the distributive property, you need to multiply each term inside the parentheses with the term outside the parentheses. For example, if you have the expression $2x(-11x - 7)$, you would multiply $2x$ with $-11x$ and $-7$ separately.

Q: What is the difference between the distributive property and the commutative property?

A: The distributive property allows us to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses. The commutative property, on the other hand, allows us to rearrange the order of terms in an expression without changing its value.

Q: Can I simplify an expression by combining like terms?

A: Yes, you can simplify an expression by combining like terms. Like terms are terms that have the same variable and exponent. For example, if you have the expression $2x^2 + 3x^2$, you can combine the like terms to get $5x^2$.

Q: What is the correct order of operations when simplifying an expression?

A: The correct order of operations when simplifying an expression is:

1. Parentheses: Evaluate 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.

Q: Can I use the distributive property to simplify expressions with fractions?

A: Yes, you can use the distributive property to simplify expressions with fractions. For example, if you have the expression $\frac{2x}{3}(-11x - 7)$, you would multiply $\frac{2x}{3}$ with $-11x$ and $-7$ separately.

Q: What are some common mistakes to avoid when simplifying expressions?

A: Some common mistakes to avoid when simplifying expressions include:

• Forgetting to apply the distributive property
• Not combining like terms
• Not following the correct order of operations
• Making errors when multiplying or dividing fractions

Tips and Tricks

• Always read the problem carefully and understand what is being asked.
• Use the distributive property to expand expressions and then combine like terms.
• Follow the correct order of operations to ensure that you are simplifying the expression correctly.
• Check your work by plugging in values or using a calculator to verify your answer.

Common Misconceptions

• Some students may think that the distributive property only applies to multiplication and division, but it can also be used to simplify expressions with addition and subtraction.
• Some students may think that they can simplify expressions by combining like terms without applying the distributive property first.
• Some students may think that the order of operations is always the same, but it can vary depending on the specific problem.

Conclusion

In conclusion, simplifying expressions is an important skill in algebra that requires attention to detail and a clear understanding of the distributive property and the order of operations. By following the tips and tricks outlined in this article, you can avoid common mistakes and ensure that you are simplifying expressions correctly.

Additional Resources

For more information on simplifying expressions and applying the distributive property, please refer to the following resources:

• Algebra Tutorial
• Distributive Property
• Simplifying Expressions

Practice Problems

To practice simplifying expressions and applying the distributive property, please try the following problems:

• Simplify the expression $3x(2x + 5)$.
• Simplify the expression $4x(-2x + 3)$.
• Simplify the expression $2x(3x - 2)$.

Answer Key

• $6x^2 + 15x$
• $-8x^2 + 12x$
• $6x^2 - 4x$