(7x-6y)×3z = If You Will Answer I Will ​

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Introduction

Mathematics is a fascinating subject that involves solving equations, inequalities, and other mathematical problems. One of the fundamental concepts in mathematics is the distributive property, which states that for any real numbers a, b, and c, the following equation holds: a(b + c) = ab + ac. In this article, we will explore the distributive property and how it can be applied to solve equations involving variables.

Understanding the Distributive Property

The distributive property is a fundamental concept in mathematics that allows us to expand expressions involving variables. It states that for any real numbers a, b, and c, the following equation holds: a(b + c) = ab + ac. This means that we can distribute the variable a to both b and c, and then combine the results.

For example, consider the equation 2(x + 3). Using the distributive property, we can expand this expression as follows:

2(x + 3) = 2x + 6

In this example, we distributed the variable 2 to both x and 3, and then combined the results.

Applying the Distributive Property to the Given Equation

Now, let's apply the distributive property to the given equation (7x-6y)×3z. Using the distributive property, we can expand this expression as follows:

(7x-6y)×3z = 7x(3z) - 6y(3z)

Using the distributive property again, we can expand the expressions 7x(3z) and -6y(3z) as follows:

7x(3z) = 21xz -6y(3z) = -18yz

Now, we can combine the results:

(7x-6y)×3z = 21xz - 18yz

Conclusion

In this article, we explored the distributive property and how it can be applied to solve equations involving variables. We used the distributive property to expand the given equation (7x-6y)×3z and arrived at the solution 21xz - 18yz. The distributive property is a fundamental concept in mathematics that allows us to expand expressions involving variables, and it is an essential tool for solving equations and inequalities.

Frequently Asked Questions

  • Q: What is the distributive property? A: The distributive property is a fundamental concept in mathematics that allows us to expand expressions involving variables. It states that for any real numbers a, b, and c, the following equation holds: a(b + c) = ab + ac.
  • Q: How can I apply the distributive property to solve equations? A: To apply the distributive property, simply distribute the variable to both terms inside the parentheses, and then combine the results.
  • Q: What is the solution to the equation (7x-6y)×3z? A: The solution to the equation (7x-6y)×3z is 21xz - 18yz.

Additional Resources

  • Khan Academy: Distributive Property
  • Mathway: Distributive Property
  • Wolfram Alpha: Distributive Property

Final Thoughts

The distributive property is a fundamental concept in mathematics that allows us to expand expressions involving variables. It is an essential tool for solving equations and inequalities, and it is used extensively in algebra and other branches of mathematics. By understanding and applying the distributive property, you can solve a wide range of mathematical problems and become a proficient mathematician.

Introduction

In our previous article, we explored the distributive property and how it can be applied to solve equations involving variables. We used the distributive property to expand the given equation (7x-6y)×3z and arrived at the solution 21xz - 18yz. In this article, we will answer some frequently asked questions related to the distributive property and provide additional resources for further learning.

Q&A

Q: What is the distributive property?

A: The distributive property is a fundamental concept in mathematics that allows us to expand expressions involving variables. It states that for any real numbers a, b, and c, the following equation holds: a(b + c) = ab + ac.

Q: How can I apply the distributive property to solve equations?

A: To apply the distributive property, simply distribute the variable to both terms inside the parentheses, and then combine the results. For example, consider the equation 2(x + 3). Using the distributive property, we can expand this expression as follows:

2(x + 3) = 2x + 6

Q: What is the solution to the equation (7x-6y)×3z?

A: The solution to the equation (7x-6y)×3z is 21xz - 18yz.

Q: Can I use the distributive property to solve equations with more than two variables?

A: Yes, you can use the distributive property to solve equations with more than two variables. For example, consider the equation (2x + 3y) × (4z + 5w). Using the distributive property, we can expand this expression as follows:

(2x + 3y) × (4z + 5w) = 8xz + 10xw + 12yz + 15yw

Q: How can I use the distributive property to simplify expressions?

A: To use the distributive property to simplify expressions, simply distribute the variable to both terms inside the parentheses, and then combine the results. For example, consider the expression 3(2x + 5). Using the distributive property, we can expand this expression as follows:

3(2x + 5) = 6x + 15

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 distribute the variable to both terms inside the parentheses
  • Not combining like terms after distributing the variable
  • Using the distributive property incorrectly, such as distributing a variable to a single term instead of both terms inside the parentheses

Additional Resources

  • Khan Academy: Distributive Property
  • Mathway: Distributive Property
  • Wolfram Alpha: Distributive Property
  • Algebra.com: Distributive Property
  • Purplemath: Distributive Property

Final Thoughts

The distributive property is a fundamental concept in mathematics that allows us to expand expressions involving variables. It is an essential tool for solving equations and inequalities, and it is used extensively in algebra and other branches of mathematics. By understanding and applying the distributive property, you can solve a wide range of mathematical problems and become a proficient mathematician.

Practice Problems

  • Expand the expression (4x + 2y) × (3z + 5w)
  • Simplify the expression 2(3x + 4)
  • Solve the equation (x + 2y) × (4z + 5w) = 12xz + 20yw

Solutions

  • (4x + 2y) × (3z + 5w) = 12xz + 15xw + 6yz + 10yw
  • 2(3x + 4) = 6x + 8
  • (x + 2y) × (4z + 5w) = 4xz + 5xw + 8yz + 10yw