Simplify The Expression:\[$(y + 5) + 9y\$\]

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Introduction

In algebra, simplifying expressions is a crucial skill that helps us solve equations and inequalities. It involves combining like terms and removing any unnecessary components from the expression. In this article, we will simplify the expression $(y + 5) + 9y$ using basic algebraic rules.

Understanding the Expression

The given expression is $(y + 5) + 9y$. To simplify this expression, we need to understand the concept of like terms. Like terms are terms that have the same variable raised to the same power. In this case, the like terms are $y$ and $9y$.

Simplifying the Expression

To simplify the expression, we will use the distributive property, which states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. We can rewrite the expression as:

$$(y + 5) + 9y = y + 5 + 9y$$

Now, we can combine the like terms $y$ and $9y$ by adding their coefficients. The coefficient of $y$ is $1$, and the coefficient of $9y$ is $9$. Therefore, we can add them as follows:

$$y + 5 + 9y = (1 + 9)y + 5$$

Using the distributive property, we can simplify the expression further:

$$(1 + 9)y + 5 = 10y + 5$$

Therefore, the simplified expression is $10y + 5$.

Conclusion

In this article, we simplified the expression $(y + 5) + 9y$ using basic algebraic rules. We identified the like terms, combined them using the distributive property, and removed any unnecessary components from the expression. The simplified expression is $10y + 5$. This skill is essential in algebra, as it helps us solve equations and inequalities.

Example Problems

Problem 1

Simplify the expression $(x + 2) + 7x$.

Solution

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

$$(x + 2) + 7x = x + 2 + 7x$$

Now, we can combine the like terms $x$ and $7x$ by adding their coefficients. The coefficient of $x$ is $1$, and the coefficient of $7x$ is $7$. Therefore, we can add them as follows:

$$x + 2 + 7x = (1 + 7)x + 2$$

Using the distributive property, we can simplify the expression further:

$$(1 + 7)x + 2 = 8x + 2$$

Therefore, the simplified expression is $8x + 2$.

Problem 2

Simplify the expression $(y - 3) + 4y$.

Solution

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

$$(y - 3) + 4y = y - 3 + 4y$$

Now, we can combine the like terms $y$ and $4y$ by adding their coefficients. The coefficient of $y$ is $1$, and the coefficient of $4y$ is $4$. Therefore, we can add them as follows:

$$y - 3 + 4y = (1 + 4)y - 3$$

Using the distributive property, we can simplify the expression further:

$$(1 + 4)y - 3 = 5y - 3$$

Therefore, the simplified expression is $5y - 3$.

Tips and Tricks

• When simplifying expressions, always look for like terms and combine them using the distributive property.
• Use the distributive property to rewrite the expression and make it easier to simplify.
• Be careful when combining like terms, as the coefficients must be added correctly.

Common Mistakes

• Failing to identify like terms and combine them correctly.
• Not using the distributive property to rewrite the expression.
• Adding or subtracting coefficients incorrectly.

Conclusion

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Introduction

In our previous article, we simplified the expression $(y + 5) + 9y$ using basic algebraic rules. In this article, we will answer some frequently asked questions about simplifying expressions.

Q&A

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, $y$ and $9y$ are like terms because they both have the variable $y$ raised to the power of 1.

Q: How do I identify like terms?

A: To identify like terms, look for terms that have the same variable raised to the same power. For example, in the expression $(y + 5) + 9y$, the like terms are $y$ and $9y$.

Q: What is the distributive property?

A: The distributive property is a rule that states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. This means that we can distribute the multiplication over the addition.

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

A: To use the distributive property to simplify expressions, rewrite the expression by distributing the multiplication over the addition. For example, in the expression $(y + 5) + 9y$, we can rewrite it as:

$$(y + 5) + 9y = y + 5 + 9y$$

Now, we can combine the like terms $y$ and $9y$ by adding their coefficients.

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

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

• Failing to identify like terms and combine them correctly.
• Not using the distributive property to rewrite the expression.
• Adding or subtracting coefficients incorrectly.

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

A: An expression is simplified when there are no like terms left to combine. In other words, when we have combined all the like terms, the expression is simplified.

Q: Can you give me some examples of simplifying expressions?

A: Yes, here are some examples of simplifying expressions:

• Simplify the expression $(x + 2) + 7x$.
• Simplify the expression $(y - 3) + 4y$.

Q: How do 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 algebra textbooks to find practice problems.
• Work with a partner or tutor to get feedback on your work.

Tips and Tricks

• Always look for like terms and combine them using the distributive property.
• Use the distributive property to rewrite the expression and make it easier to simplify.
• Be careful when combining like terms, as the coefficients must be added correctly.

Common Mistakes

• Failing to identify like terms and combine them correctly.
• Not using the distributive property to rewrite the expression.
• Adding or subtracting coefficients incorrectly.

Conclusion

Simplifying expressions is a crucial skill in algebra that helps us solve equations and inequalities. By identifying like terms, combining them using the distributive property, and removing any unnecessary components from the expression, we can simplify expressions and make them easier to work with. Remember to always look for like terms, use the distributive property, and be careful when combining coefficients. With practice and patience, you will become proficient in simplifying expressions and solving equations and inequalities.