Simplify The Expression $4(2x - 8y) + 3y$.

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Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for any math enthusiast. In this article, we will focus on simplifying the expression $4(2x - 8y) + 3y$. We will break down the process into manageable steps, using a combination of mathematical rules and techniques to arrive at the simplified expression.

Understanding the Expression

Before we dive into the simplification process, let's take a closer look at the given expression. The expression is a combination of two terms: $4(2x - 8y)$ and $3y$. The first term is a product of a constant (4) and a binomial (2x - 8y), while the second term is a simple variable term (3y).

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+aca(b + c) = ab + ac

Using this property, we can expand the first term in the expression:

4(2x−8y)=4⋅2x−4⋅8y4(2x - 8y) = 4 \cdot 2x - 4 \cdot 8y

Simplifying the First Term

Now that we have expanded the first term, we can simplify it further. We can start by multiplying the constants:

4â‹…2x=8x4 \cdot 2x = 8x

4â‹…8y=32y4 \cdot 8y = 32y

So, the first term becomes:

8x−32y8x - 32y

Combining Like Terms

Now that we have simplified the first term, we can combine it with the second term. To do this, we need to identify like terms, which are terms that have the same variable raised to the same power. In this case, we have two like terms: $8x$ and $-32y$.

Simplifying the Expression

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

8x−32y+3y8x - 32y + 3y

Final Simplification

The final step in simplifying the expression is to combine the like terms:

8x−29y8x - 29y

And that's it! We have successfully simplified the expression $4(2x - 8y) + 3y$.

Conclusion

Simplifying algebraic expressions is an essential skill for any math enthusiast. By applying the distributive property, simplifying terms, and combining like terms, we can arrive at the simplified expression. In this article, we have walked through the process of simplifying the expression $4(2x - 8y) + 3y$, and we have arrived at the final simplified expression: $8x - 29y$.

Tips and Tricks

  • When simplifying algebraic expressions, always start by applying the distributive property.
  • Identify like terms and combine them to simplify the expression.
  • Use the order of operations (PEMDAS) to ensure that you are simplifying the expression correctly.

Common Mistakes

  • Failing to apply the distributive property.
  • Not identifying like terms.
  • Not combining like terms.

Real-World Applications

Simplifying algebraic expressions has many real-world applications. For example, in physics, algebraic expressions are used to describe the motion of objects. In engineering, algebraic expressions are used to design and optimize systems. In economics, algebraic expressions are used to model and analyze economic systems.

Final Thoughts

Simplifying algebraic expressions is an essential skill for any math enthusiast. By applying the distributive property, simplifying terms, and combining like terms, we can arrive at the simplified expression. In this article, we have walked through the process of simplifying the expression $4(2x - 8y) + 3y$, and we have arrived at the final simplified expression: $8x - 29y$. We hope that this article has provided you with a better understanding of how to simplify algebraic expressions and has inspired you to explore the world of mathematics.

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Introduction

In our previous article, we walked through the process of simplifying the expression $4(2x - 8y) + 3y$. We applied the distributive property, simplified terms, and combined like terms to arrive at the final simplified expression: $8x - 29y$. In this article, we will answer some of the most frequently asked questions about simplifying algebraic expressions.

Q&A

Q: What is the distributive property, and how is it used in simplifying algebraic expressions?

A: The distributive property is a mathematical rule that states that for any real numbers a, b, and c, the following equation holds:

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

This property is used to expand expressions that involve the product of a constant and a binomial.

Q: How do I identify like terms in an algebraic expression?

A: Like terms are terms that have the same variable raised to the same power. To identify like terms, look for terms that have the same variable and exponent. For example, in the expression $2x + 3x$, the terms $2x$ and $3x$ are like terms because they both have the variable x raised to the power of 1.

Q: How do I combine like terms in an algebraic expression?

A: To combine like terms, add or subtract the coefficients of the like terms. For example, in the expression $2x + 3x$, the coefficients of the like terms are 2 and 3. To combine these terms, add the coefficients: $2 + 3 = 5$. The resulting expression is $5x$.

Q: What is the order of operations, and how is it used in simplifying algebraic expressions?

A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. The order of operations is:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify an algebraic expression that involves fractions?

A: To simplify an algebraic expression that involves fractions, follow these steps:

  1. Multiply the numerator and denominator by the least common multiple (LCM) of the denominators.
  2. Simplify the resulting expression by combining like terms.
  3. Cancel out any common factors between the numerator and denominator.

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

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

  • Failing to apply the distributive property.
  • Not identifying like terms.
  • Not combining like terms.
  • Not following the order of operations.

Tips and Tricks

  • Always start by applying the distributive property.
  • Identify like terms and combine them to simplify the expression.
  • Use the order of operations to ensure that you are simplifying the expression correctly.
  • Be careful when simplifying expressions that involve fractions.

Real-World Applications

Simplifying algebraic expressions has many real-world applications. For example, in physics, algebraic expressions are used to describe the motion of objects. In engineering, algebraic expressions are used to design and optimize systems. In economics, algebraic expressions are used to model and analyze economic systems.

Final Thoughts

Simplifying algebraic expressions is an essential skill for any math enthusiast. By applying the distributive property, simplifying terms, and combining like terms, we can arrive at the simplified expression. In this article, we have answered some of the most frequently asked questions about simplifying algebraic expressions and have provided tips and tricks for simplifying expressions. We hope that this article has provided you with a better understanding of how to simplify algebraic expressions and has inspired you to explore the world of mathematics.