Rewrite In Simplest Terms: 4 ( − P − 3 Q ) + 9 Q − 10 ( 6 Q + 3 P 4(-p - 3q) + 9q - 10(6q + 3p 4 ( − P − 3 Q ) + 9 Q − 10 ( 6 Q + 3 P ]Answer: □ \square □

Introduction

Algebraic expressions can be complex and daunting, but with the right techniques, they can be simplified to reveal their underlying structure. In this article, we will explore how to simplify the expression $4(-p - 3q) + 9q - 10(6q + 3p)$ using basic algebraic rules.

Understanding the Expression

Before we dive into simplifying the expression, let's take a closer look at what it represents. The expression consists of three main parts:

1. $4(-p - 3q)$: This part involves multiplying a constant (4) by a binomial (-p - 3q).
2. $9q$: This is a simple term that involves multiplying a constant (9) by a variable (q).
3. $-10(6q + 3p)$: This part involves multiplying a constant (-10) by a binomial (6q + 3p).

Step 1: Distribute the Constants

To simplify the expression, we need to distribute the constants to each term within the parentheses. This involves multiplying each constant by each term inside the parentheses.

4(-p - 3q) = -4p - 12q
9q = 9q
-10(6q + 3p) = -60q - 30p

Step 2: Combine Like Terms

Now that we have distributed the constants, we can combine like terms. Like terms are terms that have the same variable(s) raised to the same power.

-4p - 12q + 9q - 60q - 30p

We can combine the like terms by adding or subtracting their coefficients.

-4p - 3q - 30p - 60q

Step 3: Combine the Like Terms Further

We can combine the like terms further by adding or subtracting their coefficients.

-34p - 63q

Conclusion

In this article, we have simplified the expression $4(-p - 3q) + 9q - 10(6q + 3p)$ using basic algebraic rules. We distributed the constants to each term within the parentheses and then combined like terms to reveal the underlying structure of the expression. The simplified expression is $-34p - 63q$.

Tips and Tricks

• When simplifying algebraic expressions, it's essential to distribute the constants to each term within the parentheses.
• Combining like terms is a crucial step in simplifying algebraic expressions.
• Make sure to check your work by plugging in values for the variables to ensure that the expression is indeed simplified.

Common Mistakes to Avoid

• Failing to distribute the constants to each term within the parentheses.
• Not combining like terms correctly.
• Not checking the work by plugging in values for the variables.

Real-World Applications

Simplifying algebraic expressions is a fundamental skill that has numerous real-world applications. In mathematics, it's used to solve equations and inequalities, while in science and engineering, it's used to model real-world phenomena and make predictions.

Final Thoughts

Introduction

In our previous article, we explored how to simplify the expression $4(-p - 3q) + 9q - 10(6q + 3p)$ using basic algebraic rules. In this article, we will answer some of the most frequently asked questions about simplifying algebraic expressions.

Q: What is the first step in simplifying an algebraic expression?

A: The first step in simplifying an algebraic expression is to distribute the constants to each term within the parentheses. This involves multiplying each constant by each term inside the parentheses.

Q: How do I know which terms to combine?

A: To combine like terms, you need to identify the terms that have the same variable(s) raised to the same power. For example, in the expression $-4p - 12q + 9q - 60q - 30p$, the like terms are $-4p$ and $-30p$, and the like terms are $-12q$, $9q$, and $-60q$.

Q: Can I combine terms that have different variables?

A: No, you cannot combine terms that have different variables. For example, in the expression $-4p - 12q + 9q - 60q - 30p$, you cannot combine the terms $-4p$ and $-12q$ because they have different variables.

Q: How do I check my work when simplifying an algebraic expression?

A: To check your work, plug in values for the variables and evaluate the expression. For example, if you simplify the expression $4(-p - 3q) + 9q - 10(6q + 3p)$ to $-34p - 63q$, you can plug in values for $p$ and $q$ to check that the expression is indeed simplified.

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 distribute the constants to each term within the parentheses.
• Not combining like terms correctly.
• Not checking the work by plugging in values for the variables.

Q: How do I simplify an algebraic expression with multiple parentheses?

A: To simplify an algebraic expression with multiple parentheses, follow the order of operations (PEMDAS):

1. Evaluate the expressions inside the parentheses.
2. Distribute the constants to each term within the parentheses.
3. Combine like terms.

Q: Can I simplify an algebraic expression with variables in the denominator?

A: Yes, you can simplify an algebraic expression with variables in the denominator. However, you need to be careful when simplifying expressions with variables in the denominator, as you may need to multiply both the numerator and the denominator by the same value to eliminate the variable in the denominator.

Q: How do I simplify an algebraic expression with fractions?

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

1. Simplify the fractions by finding the greatest common divisor (GCD) of the numerator and the denominator.
2. Combine like terms.
3. Check the work by plugging in values for the variables.

Conclusion

Simplifying algebraic expressions is a fundamental skill that has numerous real-world applications. By following the steps outlined in this article, you can simplify even the most complex expressions and reveal their underlying structure. Remember to distribute the constants, combine like terms, and check your work to ensure that the expression is indeed simplified.

Tips and Tricks

• When simplifying algebraic expressions, it's essential to distribute the constants to each term within the parentheses.
• Combining like terms is a crucial step in simplifying algebraic expressions.
• Make sure to check your work by plugging in values for the variables to ensure that the expression is indeed simplified.

Real-World Applications

Simplifying algebraic expressions is a fundamental skill that has numerous real-world applications. In mathematics, it's used to solve equations and inequalities, while in science and engineering, it's used to model real-world phenomena and make predictions.

Final Thoughts

Simplifying algebraic expressions may seem daunting at first, but with practice and patience, it becomes second nature. By following the steps outlined in this article, you can simplify even the most complex expressions and reveal their underlying structure. Remember to distribute the constants, combine like terms, and check your work to ensure that the expression is indeed simplified.