Type The Correct Answer In Each Box. Use Numerals Instead Of Words.Consider This Expression: { (x+5)(x-7)$} . C O M P L E T E T H E B O X T O S H O W T H E D I S T R I B U T I V E P R O P E R T Y A P P L I E D T O T H I S E X P R E S S I O N . .Complete The Box To Show The Distributive Property Applied To This Expression. . C O M Pl E T E T H E B O X T Os H O Wt H E D I S T R Ib U T I V E P Ro P Er T Y A Ppl I E D T O T Hi Se X P Ress I O N . [ \begin{tabular}{l|c|c|} \multicolumn{1}{c}{} &

Understanding 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. In this article, we will explore how to apply the distributive property to the given expression: {(x+5)(x-7)$}$.

The Distributive Property Formula

The distributive property formula is:

a(b + c) = ab + ac

where a, b, and c are algebraic expressions.

Applying the Distributive Property to the Given Expression

To apply the distributive property to the given expression, we need to multiply each term inside the parentheses with the term outside.

{(x+5)(x-7)$}$

Using the distributive property formula, we can expand the expression as follows:

{x(x-7) + 5(x-7)$}$

Expanding the Expression

Now, let's expand the expression further by multiplying each term inside the parentheses with the term outside.

{x(x-7) + 5(x-7)$}$

= {x^2 - 7x + 5x - 35$}$

Simplifying the Expression

Now, let's simplify the expression by combining like terms.

{x^2 - 7x + 5x - 35$}$

= {x^2 - 2x - 35$}$

Conclusion

In this article, we have applied the distributive property to the given expression: {(x+5)(x-7)$}$. We have expanded the expression using the distributive property formula and simplified it by combining like terms. The final answer is:

{x^2 - 2x - 35$}$

Discussion Category: Mathematics

This article is part of the mathematics discussion category, where we explore various concepts and techniques in algebra, geometry, and other branches of mathematics.

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 distributive property formula is: a(b + c) = ab + ac
• To apply the distributive property to an expression, we need to multiply each term inside the parentheses with the term outside.
• We can expand an expression using the distributive property formula and simplify it by combining like terms.

Practice Problems

1. Apply the distributive property to the expression: {(x-3)(x+2)$}$
2. Expand the expression: {(x+4)(x-1)$}$
3. Simplify the expression: {x^2 + 5x - 3x - 2$}$

Answer Key

1. {x^2 - 3x + 2x - 6$}$
2. {x^2 + 4x - x - 4$}$
3. {x^2 + 2x - 2$}$

References

• Algebraic Expressions
• Distributive Property
• Algebra

Related Articles

• Simplifying Algebraic Expressions
• Factoring Algebraic Expressions
• Algebraic Identities
  Frequently Asked Questions (FAQs) on the Distributive Property ================================================================

Q: What is the distributive property in algebra?

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. It is a way of multiplying a single term to two or more terms inside parentheses.

Q: How do I apply the distributive property to an expression?

A: To apply the distributive property to an expression, you need to multiply each term inside the parentheses with the term outside. For example, if you have the expression {(x+5)(x-7)$}$, you would multiply each term inside the parentheses with the term outside, like this:

{x(x-7) + 5(x-7)$}$

Q: What is the distributive property formula?

A: The distributive property formula is:

a(b + c) = ab + ac

where a, b, and c are algebraic expressions.

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

A: Yes, you can use the distributive property to simplify expressions. By expanding the expression using the distributive property formula and then combining like terms, you can simplify the expression.

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

A: To simplify an expression using the distributive property, you need to follow these steps:

1. Expand the expression using the distributive property formula.
2. Combine like terms.
3. Simplify the expression.

For example, if you have the expression {x^2 - 7x + 5x - 35$}$, you would expand it using the distributive property formula, like this:

{x^2 - 7x + 5x - 35$}$

= {x^2 - 2x - 35$}$

Q: Can I use the distributive property to factor expressions?

A: Yes, you can use the distributive property to factor expressions. By factoring out a common term from each term inside the parentheses, you can factor the expression.

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

A: To factor an expression using the distributive property, you need to follow these steps:

1. Identify a common term that can be factored out from each term inside the parentheses.
2. Factor out the common term from each term inside the parentheses.
3. Simplify the expression.

For example, if you have the expression {x^2 + 5x - 3x - 2$}$, you would factor out a common term from each term inside the parentheses, like this:

{x^2 + 5x - 3x - 2$}$

= {x^2 + 2x - 2$}$

Q: What are some common mistakes to avoid when using the distributive property?

A: Some common mistakes to avoid when using the distributive property include:

• Forgetting to multiply each term inside the parentheses with the term outside.
• Not combining like terms correctly.
• Not simplifying the expression correctly.

Q: How can I practice using the distributive property?

A: You can practice using the distributive property by working through examples and exercises. You can also try applying the distributive property to different types of expressions, such as quadratic expressions and polynomial expressions.

Q: What are some real-world applications of the distributive property?

A: The distributive property has many real-world applications, including:

• Algebraic geometry: The distributive property is used to expand and simplify algebraic expressions in algebraic geometry.
• Computer science: The distributive property is used in computer science to optimize algorithms and data structures.
• Engineering: The distributive property is used in engineering to design and analyze complex systems.

Q: Can I use the distributive property to solve equations?

A: Yes, you can use the distributive property to solve equations. By expanding and simplifying the equation using the distributive property, you can solve for the variable.

Q: How do I use the distributive property to solve equations?

A: To use the distributive property to solve equations, you need to follow these steps:

1. Expand the equation using the distributive property formula.
2. Simplify the equation.
3. Solve for the variable.

For example, if you have the equation {x^2 - 7x + 5x - 35 = 0$}$, you would expand it using the distributive property formula, like this:

{x^2 - 7x + 5x - 35 = 0$}$

= {x^2 - 2x - 35 = 0$}$

Q: Can I use the distributive property to solve inequalities?

A: Yes, you can use the distributive property to solve inequalities. By expanding and simplifying the inequality using the distributive property, you can solve for the variable.

Q: How do I use the distributive property to solve inequalities?

A: To use the distributive property to solve inequalities, you need to follow these steps:

1. Expand the inequality using the distributive property formula.
2. Simplify the inequality.
3. Solve for the variable.

For example, if you have the inequality {x^2 - 7x + 5x - 35 > 0$}$, you would expand it using the distributive property formula, like this:

{x^2 - 7x + 5x - 35 > 0$}$

= {x^2 - 2x - 35 > 0$}$

Conclusion

In this article, we have answered some frequently asked questions about the distributive property. We have covered topics such as how to apply the distributive property, how to simplify expressions using the distributive property, and how to factor expressions using the distributive property. We have also covered some common mistakes to avoid when using the distributive property and some real-world applications of the distributive property.