Add The Following Expressions:1. { (-15 X Z + 4 X Y) + (20 X Y - 9 Y Z + 16 X Z)$}$Choose The Correct Simplified Expression:A. ${ 24 X^2 Y^2 - 9 Y Z + X^2 Z^2\$} B. ${ 24 X Y - 9 Y Z + X Z\$} C. ${ 16 X Y Z\$} D.

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is a crucial skill to master. In this article, we will explore how to simplify a given algebraic expression, using the expression {(-15 x z + 4 x y) + (20 x y - 9 y z + 16 x z)$}$ as an example. We will break down the expression into smaller parts, apply the rules of algebra, and arrive at the simplified form.

Step 1: Distributive Property

The first step in simplifying the expression is to apply the distributive property. This property states that for any real numbers a, b, and c, the following equation holds:

a(b + c) = ab + ac

Using this property, we can rewrite the given expression as:

{(-15 x z + 4 x y) + (20 x y - 9 y z + 16 x z)$ = (-15 x z + 4 x y) + (20 x y - 9 y z) + (16 x z)$

Step 2: Combine Like Terms

The next step is to combine like terms. Like terms are terms that have the same variable(s) raised to the same power. In this case, we have the following like terms:

• ${-15 x z}$ and ${16 x z}$
• ${4 x y}$ and ${20 x y}$
• ${-9 y z}$

We can combine these like terms by adding or subtracting their coefficients. For example, we can combine ${-15 x z}$ and ${16 x z}$ as follows:

${-15 x z + 16 x z = (16 - 15) x z = x z}$

Similarly, we can combine ${4 x y}$ and ${20 x y}$ as follows:

${4 x y + 20 x y = (4 + 20) x y = 24 x y}$

Finally, we can combine ${-9 y z}$ as is, since it does not have a like term to combine with.

Step 3: Simplify the Expression

Now that we have combined like terms, we can simplify the expression by combining the remaining terms. We have the following terms:

• ${24 x y}$
• ${-9 y z}$
• ${x z}$

We can combine these terms as follows:

${24 x y - 9 y z + x z}$

Conclusion

In conclusion, we have simplified the given algebraic expression using the distributive property and combining like terms. The simplified expression is:

[24 x y - 9 y z + x z\$}

This expression is the correct answer among the given options.

Answer

The correct answer is:

${24 x y - 9 y z + x z\$}

Discussion

This problem requires the application of algebraic properties, such as the distributive property and combining like terms. It also requires careful attention to detail and the ability to simplify complex expressions.

Related Topics

• Distributive Property
• Combining Like Terms
• Algebraic Expressions
• Simplifying Equations

Example Problems

• Simplify the expression {(2 x y + 3 x z) + (4 x y - 5 y z)$}$
• Simplify the expression {(6 x y - 2 x z) + (8 x y + 3 y z)$}$
• Simplify the expression {(9 x y + 4 x z) + (2 x y - 6 y z)$}$

Practice Problems

• Simplify the expression {(3 x y + 2 x z) + (5 x y - 4 y z)$}$
• Simplify the expression {(7 x y - 3 x z) + (9 x y + 2 y z)$}$
• Simplify the expression {(11 x y + 6 x z) + (4 x y - 8 y z)$}$

Conclusion

Introduction

In our previous article, we explored how to simplify algebraic expressions using the distributive property and combining like terms. In this article, we will provide a Q&A guide to help you better understand the concepts and apply them to real-world problems.

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that states that for any real numbers a, b, and c, the following equation holds:

a(b + c) = ab + ac

This property allows us to distribute a single term across the terms inside the parentheses.

Q: How do I apply the distributive property?

A: To apply the distributive property, simply multiply the term outside the parentheses by each term inside the parentheses. For example, if we have the expression (2x + 3)(4x - 2), we can apply the distributive property as follows:

(2x + 3)(4x - 2) = 2x(4x - 2) + 3(4x - 2)

Q: What is combining like terms?

A: Combining like terms is the process of adding or subtracting terms that have the same variable(s) raised to the same power. For example, if we have the expression 2x + 3x, we can combine the like terms as follows:

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

Q: How do I combine like terms?

A: To combine like terms, simply add or subtract the coefficients of the terms. For example, if we have the expression 2x + 3x - 4x, we can combine the like terms as follows:

2x + 3x - 4x = (2 + 3 - 4)x = x

Q: What is a simplified expression?

A: A simplified expression is an expression that has been reduced to its simplest form by applying the distributive property and combining like terms. For example, if we have the expression (2x + 3)(4x - 2), we can simplify it as follows:

(2x + 3)(4x - 2) = 8x^2 - 4x + 12x - 6

= 8x^2 + 8x - 6

Q: How do I know if an expression is simplified?

A: To determine if an expression is simplified, simply check if it has been reduced to its simplest form by applying the distributive property and combining like terms. If it has, then it is a simplified expression.

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

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

• Not applying the distributive property correctly
• Not combining like terms correctly
• Not simplifying expressions fully
• Not checking for errors in the simplification process

Q: How can I practice simplifying expressions?

A: To practice simplifying expressions, try the following:

• Start with simple expressions and gradually move on to more complex ones
• Use online resources or worksheets to practice simplifying expressions
• Work with a partner or tutor to get feedback on your simplification skills
• Take your time and double-check your work to ensure accuracy

Conclusion

In conclusion, simplifying algebraic expressions is a crucial skill in mathematics. By applying the distributive property and combining like terms, we can simplify complex expressions and arrive at the correct answer. We hope this Q&A guide has provided a clear and concise overview of the concepts and helped you better understand how to simplify algebraic expressions.