Simplify The Expression:${ 5(x+2) - 2 }$

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Introduction

Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. In this article, we will focus on simplifying the given expression: $5(x+2) - 2$. We will break down the expression step by step, using the distributive property and combining like terms to arrive at the simplified form.

Understanding the Distributive Property

The distributive property is a fundamental concept in algebra that allows us to expand expressions involving multiplication and addition. It states that for any real numbers $a$, $b$, and $c$, the following equation holds:

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

In the given expression, we have $5(x+2)$, which can be expanded using the distributive property. We will multiply the constant $5$ by each term inside the parentheses, $x$ and $2$.

Applying the Distributive Property

Using the distributive property, we can rewrite the expression as:

$5(x+2) = 5x + 5(2)$

Now, we can simplify the expression further by multiplying $5$ by $2$, which gives us:

$5(x+2) = 5x + 10$

Combining Like Terms

Now that we have expanded the expression, we can combine like terms to simplify it further. In this case, we have two terms, $5x$ and $-2$, which are like terms because they both contain the variable $x$. We can combine these terms by adding or subtracting their coefficients.

Simplifying the Expression

To simplify the expression, we need to combine the like terms $5x$ and $-2$. We can do this by adding their coefficients, which gives us:

$5x - 2$

However, we need to be careful when combining like terms. If the coefficients have different signs, we need to subtract the smaller coefficient from the larger one.

Final Simplified Form

After combining the like terms, we arrive at the final simplified form of the expression:

$5x - 2$

This is the simplest form of the given expression, and it cannot be simplified further.

Conclusion

In this article, we simplified the expression $5(x+2) - 2$ using the distributive property and combining like terms. We broke down the expression step by step, using the distributive property to expand the expression and combining like terms to simplify it further. The final simplified form of the expression is $5x - 2$. This article demonstrates the importance of understanding the distributive property and combining like terms in simplifying algebraic expressions.

Tips and Tricks

• When simplifying expressions, always look for like terms and combine them.
• Use the distributive property to expand expressions involving multiplication and addition.
• Be careful when combining like terms, especially when the coefficients have different signs.

Frequently Asked Questions

• Q: What is the distributive property? A: The distributive property is a fundamental concept in algebra that allows us to expand expressions involving multiplication and addition.
• Q: How do I simplify expressions using the distributive property? A: To simplify expressions using the distributive property, multiply the constant by each term inside the parentheses and then combine like terms.
• Q: What are like terms? A: Like terms are terms that contain the same variable raised to the same power.

Further Reading

• Algebraic Expressions: A Comprehensive Guide
• Simplifying Algebraic Expressions: Tips and Tricks
• The Distributive Property: A Fundamental Concept in Algebra
  

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Introduction

In our previous article, we simplified the expression $5(x+2) - 2$ using the distributive property and combining like terms. We broke down the expression step by step, using the distributive property to expand the expression and combining like terms to simplify it further. In this article, we will answer some frequently asked questions related to simplifying algebraic expressions.

Q&A

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that allows us to expand expressions involving multiplication and addition. It states that for any real numbers $a$, $b$, and $c$, the following equation holds:

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

Q: How do I simplify expressions using the distributive property?

A: To simplify expressions using the distributive property, multiply the constant by each term inside the parentheses and then combine like terms. For example, in the expression $5(x+2)$, we would multiply $5$ by $x$ and $2$ to get $5x + 10$.

Q: What are like terms?

A: Like terms are terms that contain the same variable raised to the same power. For example, in the expression $5x + 3x$, $5x$ and $3x$ are like terms because they both contain the variable $x$ raised to the power of $1$.

Q: How do I combine like terms?

A: To combine like terms, add or subtract their coefficients. For example, in the expression $5x + 3x$, we would add the coefficients $5$ and $3$ to get $8x$.

Q: What is the difference between the distributive property and combining like terms?

A: The distributive property is used to expand expressions involving multiplication and addition, while combining like terms is used to simplify expressions by adding or subtracting terms with the same variable raised to the same power.

Q: Can I simplify expressions with variables in the denominator?

A: Yes, you can simplify expressions with variables in the denominator by multiplying the numerator and denominator by the same variable. For example, in the expression $\frac{x}{x+2}$, we would multiply the numerator and denominator by $x+2$ to get $\frac{x(x+2)}{(x+2)^2}$.

Q: How do I simplify expressions with fractions?

A: To simplify expressions with fractions, multiply the numerator and denominator by the same variable or number. For example, in the expression $\frac{5x}{2}$, we would multiply the numerator and denominator by $2$ to get $\frac{10x}{4}$.

Q: Can I simplify expressions with exponents?

A: Yes, you can simplify expressions with exponents by using the rules of exponents. For example, in the expression $x^2 + 3x^2$, we would combine the like terms to get $4x^2$.

Conclusion

In this article, we answered some frequently asked questions related to simplifying algebraic expressions. We covered topics such as the distributive property, combining like terms, and simplifying expressions with variables in the denominator, fractions, and exponents. We hope that this article has been helpful in clarifying any doubts you may have had about simplifying algebraic expressions.

Tips and Tricks

• Always look for like terms and combine them.
• Use the distributive property to expand expressions involving multiplication and addition.
• Be careful when combining like terms, especially when the coefficients have different signs.
• Simplify expressions with variables in the denominator by multiplying the numerator and denominator by the same variable.
• Simplify expressions with fractions by multiplying the numerator and denominator by the same variable or number.
• Simplify expressions with exponents by using the rules of exponents.

Further Reading

• Algebraic Expressions: A Comprehensive Guide
• Simplifying Algebraic Expressions: Tips and Tricks
• The Distributive Property: A Fundamental Concept in Algebra
• Exponents: A Guide to Simplifying Expressions with Exponents
• Fractions: A Guide to Simplifying Expressions with Fractions