Simplify The Expression:\[$(2x + 1)(4 - 9x) - 2x(3x + 11)\$\]

$$

Introduction

In this article, we will simplify the given expression using the distributive property and combining like terms. The expression is a combination of two binomials multiplied by a trinomial, and then subtracting another binomial multiplied by a trinomial. We will break down the expression step by step to simplify it.

Step 1: Apply the Distributive Property

To simplify the expression, we will first apply the distributive property to each term. The distributive property states that for any real numbers a, b, and c:

a(b + c) = ab + ac

We will apply this property to each term in the expression.

Distributing $(2x + 1)$ to $(4 - 9x)$

Using the distributive property, we get:

$(2x + 1)(4 - 9x) = 2x(4 - 9x) + 1(4 - 9x)$

Expanding each term, we get:

$8x - 18x^2 + 4 - 9x$

Combining like terms, we get:

$-18x^2 + 8x + 4$

Distributing $-2x$ to $(3x + 11)$

Using the distributive property, we get:

$-2x(3x + 11) = -6x^2 - 22x$

Step 2: Combine Like Terms

Now that we have applied the distributive property to each term, we can combine like terms to simplify the expression.

Combining Like Terms

We have two expressions:

$-18x^2 + 8x + 4$

$-6x^2 - 22x$

To combine like terms, we add or subtract the coefficients of the same variables.

$-18x^2 + 8x + 4 - 6x^2 - 22x$

Combining like terms, we get:

$-24x^2 - 14x + 4$

Conclusion

In this article, we simplified the given expression using the distributive property and combining like terms. We broke down the expression step by step to simplify it. The final simplified expression is:

$-24x^2 - 14x + 4$

This expression is now in its simplest form.

Tips and Tricks

• When simplifying expressions, always apply the distributive property to each term.
• Combine like terms to simplify the expression.
• Use the distributive property to expand each term.
• Be careful when combining like terms, as it is easy to make mistakes.

Real-World Applications

Simplifying expressions is an important skill in mathematics, and it has many real-world applications. For example, in physics, we use algebraic expressions to describe the motion of objects. In engineering, we use algebraic expressions to design and optimize systems. In economics, we use algebraic expressions to model and analyze economic systems.

Final Thoughts

Simplifying expressions is an important skill in mathematics, and it has many real-world applications. By following the steps outlined in this article, you can simplify any expression using the distributive property and combining like terms. Remember to always apply the distributive property to each term, combine like terms, and use the distributive property to expand each term. With practice and patience, you can become proficient in simplifying expressions and apply this skill to real-world problems.

Additional Resources

• Khan Academy: Simplifying Expressions
• Mathway: Simplifying Expressions
• Wolfram Alpha: Simplifying Expressions

Frequently Asked Questions

• Q: What is the distributive property? A: The distributive property is a mathematical property that states that for any real numbers a, b, and c, a(b + c) = ab + ac.
• Q: How do I simplify an expression using the distributive property? A: To simplify an expression using the distributive property, apply the property to each term and then combine like terms.
• Q: What are like terms? A: Like terms are terms that have the same variable and exponent. For example, 2x and 4x are like terms.

References

• [1] Khan Academy. (n.d.). Simplifying Expressions. Retrieved from https://www.khanacademy.org/math/algebra/x2f6b7c/x2f6b7d
• [2] Mathway. (n.d.). Simplifying Expressions. Retrieved from https://www.mathway.com/questions/simplifying-expressions
• [3] Wolfram Alpha. (n.d.). Simplifying Expressions. Retrieved from https://www.wolframalpha.com/input/?i=simplifying+expressions
  

$$

Introduction

In our previous article, we simplified the expression $(2x + 1)(4 - 9x) - 2x(3x + 11)$ using the distributive property and combining like terms. In this article, we will answer some frequently asked questions about simplifying expressions and provide additional resources for further learning.

Q&A

Q: What is the distributive property?

A: The distributive property is a mathematical property that states that for any real numbers a, b, and c, a(b + c) = ab + ac. This property allows us to expand expressions by multiplying each term inside the parentheses by the term outside the parentheses.

Q: How do I simplify an expression using the distributive property?

A: To simplify an expression using the distributive property, apply the property to each term and then combine like terms. For example, to simplify the expression $(2x + 1)(4 - 9x)$, we would apply the distributive property as follows:

$(2x + 1)(4 - 9x) = 2x(4 - 9x) + 1(4 - 9x)$

Expanding each term, we get:

$8x - 18x^2 + 4 - 9x$

Combining like terms, we get:

$-18x^2 + 8x + 4$

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, 2x and 4x are like terms because they both have the variable x and the exponent 1. When combining like terms, we add or subtract the coefficients of the same variables.

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the same variables. For example, to combine the terms 2x and 4x, we would add their coefficients as follows:

2x + 4x = 6x

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

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

• Failing to apply the distributive property to each term
• Failing to combine like terms
• Making errors when expanding expressions
• Failing to check for like terms

Q: How do I check for like terms?

A: To check for like terms, look for terms that have the same variable and exponent. For example, in the expression 2x + 4x, we can see that both terms have the variable x and the exponent 1, so they are like terms.

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

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

• Physics: Simplifying expressions is used to describe the motion of objects.
• Engineering: Simplifying expressions is used to design and optimize systems.
• Economics: Simplifying expressions is used to model and analyze economic systems.

Additional Resources

• Khan Academy: Simplifying Expressions
• Mathway: Simplifying Expressions
• Wolfram Alpha: Simplifying Expressions
• Algebra.com: Simplifying Expressions
• Purplemath: Simplifying Expressions

Frequently Asked Questions

• Q: What is the distributive property? A: The distributive property is a mathematical property that states that for any real numbers a, b, and c, a(b + c) = ab + ac.
• Q: How do I simplify an expression using the distributive property? A: To simplify an expression using the distributive property, apply the property to each term and then combine like terms.
• Q: What are like terms? A: Like terms are terms that have the same variable and exponent.
• Q: How do I combine like terms? A: To combine like terms, add or subtract the coefficients of the same variables.

References

• [1] Khan Academy. (n.d.). Simplifying Expressions. Retrieved from https://www.khanacademy.org/math/algebra/x2f6b7c/x2f6b7d
• [2] Mathway. (n.d.). Simplifying Expressions. Retrieved from https://www.mathway.com/questions/simplifying-expressions
• [3] Wolfram Alpha. (n.d.). Simplifying Expressions. Retrieved from https://www.wolframalpha.com/input/?i=simplifying+expressions
• [4] Algebra.com. (n.d.). Simplifying Expressions. Retrieved from https://www.algebra.com/algebra/homework/simplifying-expressions/
• [5] Purplemath. (n.d.). Simplifying Expressions. Retrieved from https://www.purplemath.com/modules/simplifying.htm