Simplify The Expression:f) { (2xy - Y)(5x - 3)$}$

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Introduction

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In algebra, simplifying expressions is a crucial skill that helps us solve equations and inequalities. It involves combining like terms, removing parentheses, and rearranging the expression to make it easier to work with. In this article, we will simplify the expression $(2xy - y)(5x - 3)$ using the distributive property and combining like terms.

Understanding the Distributive Property

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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 parentheses. It states that for any real numbers $a$, $b$, and $c$, the following equation holds:

$$a(b + c) = ab + ac$$

This property can be extended to expressions with multiple terms inside the parentheses.

Applying the Distributive Property

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To simplify the expression $(2xy - y)(5x - 3)$, we will apply the distributive property by multiplying each term inside the parentheses with the term outside the parentheses.

$$(2xy - y)(5x - 3) = 2xy(5x - 3) - y(5x - 3)$$

Expanding the Expression

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Now, we will expand each term by multiplying the terms inside the parentheses with the term outside the parentheses.

$$2xy(5x - 3) = 2xy(5x) - 2xy(3)$$

$$-y(5x - 3) = -y(5x) + y(3)$$

Simplifying the Expression

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Now, we will simplify the expression by combining like terms.

$$2xy(5x) - 2xy(3) - y(5x) + y(3)$$

$$= 10x^2y - 6xy - 5xy + 3y$$

$$= 10x^2y - 11xy + 3y$$

Conclusion

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In this article, we simplified the expression $(2xy - y)(5x - 3)$ using the distributive property and combining like terms. We expanded each term by multiplying the terms inside the parentheses with the term outside the parentheses and then simplified the expression by combining like terms. The final simplified expression is $10x^2y - 11xy + 3y$.

Tips and Tricks

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• When simplifying expressions, always look for opportunities to apply the distributive property.
• When expanding expressions, make sure to multiply each term inside the parentheses with the term outside the parentheses.
• When simplifying expressions, combine like terms to make the expression easier to work with.

Practice Problems

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• Simplify the expression $(3x - 2)(2x + 5)$.
• Simplify the expression $(x + 2)(x - 3)$.
• Simplify the expression $(2x - 1)(x + 4)$.

Real-World Applications

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Simplifying expressions is a crucial skill in many real-world applications, including:

• Physics: Simplifying expressions is essential in physics to solve equations and inequalities that describe the motion of objects.
• Engineering: Simplifying expressions is crucial in engineering to design and optimize systems.
• Economics: Simplifying expressions is essential in economics to model and analyze economic systems.

Final Thoughts

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Simplifying expressions is a fundamental skill in algebra that helps us solve equations and inequalities. By applying the distributive property and combining like terms, we can simplify expressions and make them easier to work with. In this article, we simplified the expression $(2xy - y)(5x - 3)$ using the distributive property and combining like terms. We hope this article has provided you with a better understanding of how to simplify expressions and has given you the confidence to tackle more complex problems.

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Introduction

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In our previous article, we simplified the expression $(2xy - y)(5x - 3)$ using the distributive property and combining like terms. In this article, we will answer some frequently asked questions about simplifying expressions and provide additional tips and tricks to help you master this skill.

Q&A

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Q: What is the distributive property?

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 the parentheses. It states that for any real numbers $a$, $b$, and $c$, the following equation holds:

$$a(b + c) = ab + ac$$

Q: How do I apply the distributive property?

A: To apply the distributive property, you need to multiply each term inside the parentheses with the term outside the parentheses. For example, to simplify the expression $(2xy - y)(5x - 3)$, you would multiply each term inside the parentheses with the term outside the parentheses:

$$(2xy - y)(5x - 3) = 2xy(5x - 3) - y(5x - 3)$$

Q: What is the difference between the distributive property and the commutative property?

A: The distributive property and the commutative property are two different concepts in algebra. The distributive property allows us to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses, while the commutative property states that the order of the terms does not change the result. For example:

$$a(b + c) = ab + ac$$

$$a + b = b + a$$

Q: How do I simplify expressions with multiple terms inside the parentheses?

A: To simplify expressions with multiple terms inside the parentheses, you need to apply the distributive property and combine like terms. For example, to simplify the expression $(2xy - y + 3)(5x - 3)$, you would multiply each term inside the parentheses with the term outside the parentheses and then combine like terms:

$$(2xy - y + 3)(5x - 3) = 2xy(5x - 3) - y(5x - 3) + 3(5x - 3)$$

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
• Not combining like terms
• Not checking for errors in the calculation
• Not using the correct order of operations

Tips and Tricks

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• Always apply the distributive property when simplifying expressions.
• Combine like terms to make the expression easier to work with.
• Check for errors in the calculation to ensure that the expression is simplified correctly.
• Use the correct order of operations to simplify expressions.

Practice Problems

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• Simplify the expression $(3x - 2)(2x + 5)$.
• Simplify the expression $(x + 2)(x - 3)$.
• Simplify the expression $(2x - 1)(x + 4)$.

Real-World Applications

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Simplifying expressions is a crucial skill in many real-world applications, including:

• Physics: Simplifying expressions is essential in physics to solve equations and inequalities that describe the motion of objects.
• Engineering: Simplifying expressions is crucial in engineering to design and optimize systems.
• Economics: Simplifying expressions is essential in economics to model and analyze economic systems.

Final Thoughts

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Simplifying expressions is a fundamental skill in algebra that helps us solve equations and inequalities. By applying the distributive property and combining like terms, we can simplify expressions and make them easier to work with. In this article, we answered some frequently asked questions about simplifying expressions and provided additional tips and tricks to help you master this skill. We hope this article has provided you with a better understanding of how to simplify expressions and has given you the confidence to tackle more complex problems.