Type The Correct Answer In Each Box. Use Numerals Instead Of Words.Consider This Expression: { -4x^2 + 2x - 5(1 + X)$} W H A T E X P R E S S I O N I S E Q U I V A L E N T T O T H E G I V E N E X P R E S S I O N ? What Expression Is Equivalent To The Given Expression? Wha T E X P Ress I O Ni Se Q U I V A L E N Tt O T H E G I V E N E X P Ress I O N ? { \square X^2 + \square X + \square\$}

by ADMIN 390 views

===========================================================

Understanding the Given Expression

The given expression is: βˆ’4x2+2xβˆ’5(1+x){-4x^2 + 2x - 5(1 + x)}

To simplify this expression, we need to apply the distributive property and combine like terms.

Applying the Distributive Property

The distributive property states that for any real numbers a, b, and c:

a(b + c) = ab + ac

We can apply this property to the given expression by distributing the negative sign to the terms inside the parentheses:

βˆ’5(1+x)=βˆ’5(1)βˆ’5(x){-5(1 + x) = -5(1) - 5(x)}

Simplifying the Expression

Now, we can simplify the expression by combining like terms:

βˆ’4x2+2xβˆ’5(1+x)=βˆ’4x2+2xβˆ’5βˆ’5x{-4x^2 + 2x - 5(1 + x) = -4x^2 + 2x - 5 - 5x}

Combining Like Terms

We can combine the like terms by adding or subtracting the coefficients of the same variables:

βˆ’4x2+2xβˆ’5βˆ’5x=βˆ’4x2βˆ’3xβˆ’5{-4x^2 + 2x - 5 - 5x = -4x^2 - 3x - 5}

The Final Expression

The simplified expression is: βˆ’4x2βˆ’3xβˆ’5{-4x^2 - 3x - 5}

Conclusion

In this article, we have simplified the given algebraic expression by applying the distributive property and combining like terms. The final expression is: βˆ’4x2βˆ’3xβˆ’5{-4x^2 - 3x - 5}

Key Takeaways

  • Apply the distributive property to simplify expressions with parentheses.
  • Combine like terms to simplify expressions.
  • Simplify expressions by adding or subtracting coefficients of the same variables.

Practice Problems

Try simplifying the following expressions:

  1. 2x2+3xβˆ’4(2+x){2x^2 + 3x - 4(2 + x)}
  2. βˆ’3x2+2x+5(1βˆ’x){-3x^2 + 2x + 5(1 - x)}

Answer Key

  1. 2x2+3xβˆ’8βˆ’4x=2x2βˆ’xβˆ’8{2x^2 + 3x - 8 - 4x = 2x^2 - x - 8}
  2. βˆ’3x2+2x+5βˆ’5x=βˆ’3x2βˆ’3x+5{-3x^2 + 2x + 5 - 5x = -3x^2 - 3x + 5}

Additional Resources

For more practice problems and resources, visit the following websites:

  • Khan Academy: Algebra
  • Mathway: Algebra
  • IXL: Algebra

Final Thoughts

Simplifying algebraic expressions is an essential skill in mathematics. By applying the distributive property and combining like terms, we can simplify complex expressions and make them easier to work with. Practice regularly to become proficient in simplifying algebraic expressions.

===========================================================

Q: What is the distributive property in algebra?

A: The distributive property is a fundamental concept in algebra that allows us to simplify expressions by distributing a coefficient to the terms inside parentheses. It states that for any real numbers a, b, and c:

a(b + c) = ab + ac

Q: How do I apply the distributive property to simplify expressions?

A: To apply the distributive property, simply multiply the coefficient outside the parentheses to each term inside the parentheses. For example:

-5(1 + x) = -5(1) - 5(x)

Q: What is the difference between like terms and unlike terms?

A: Like terms are terms that have the same variable raised to the same power. Unlike terms are terms that have different variables or variables raised to different powers. For example:

2x and 3x are like terms because they both have the variable x raised to the power of 1.

2x and 3y are unlike terms because they have different variables.

Q: How do I combine like terms to simplify expressions?

A: To combine like terms, simply add or subtract the coefficients of the same variables. For example:

-4x^2 + 2x - 5 - 5x = -4x^2 - 3x - 5

Q: What is the order of operations in algebra?

A: The order of operations in algebra 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: How do I simplify expressions with negative coefficients?

A: To simplify expressions with negative coefficients, simply apply the distributive property and combine like terms as usual. For example:

-3x^2 + 2x - 5(1 + x) = -3x^2 + 2x - 5 - 5x

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

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

  • Forgetting to distribute coefficients to terms inside parentheses.
  • Not combining like terms correctly.
  • Not following the order of operations.

Q: How can I practice simplifying algebraic expressions?

A: You can practice simplifying algebraic expressions by working through practice problems and exercises. Some online resources include:

  • Khan Academy: Algebra
  • Mathway: Algebra
  • IXL: Algebra

Q: What are some real-world applications of simplifying algebraic expressions?

A: Simplifying algebraic expressions has many real-world applications, including:

  • Solving systems of equations in physics and engineering.
  • Modeling population growth and decay in biology.
  • Analyzing data in statistics and data science.

Q: How can I improve my skills in simplifying algebraic expressions?

A: To improve your skills in simplifying algebraic expressions, practice regularly and seek help when needed. Some tips include:

  • Start with simple expressions and gradually move on to more complex ones.
  • Use online resources and practice problems to reinforce your understanding.
  • Seek help from teachers, tutors, or online communities when you get stuck.