Simplify The Expression: 2(p-4)-\left(p^2+3p-6\right ]

Introduction

In algebra, simplifying expressions is a crucial skill that helps us solve equations and inequalities. In this article, we will focus on simplifying the given expression: $2(p-4)-\left(p^2+3p-6\right)$. We will break down the expression into smaller parts, apply the distributive property, and combine like terms to simplify it.

Understanding the Expression

The given expression is a combination of two terms: $2(p-4)$ and $-\left(p^2+3p-6\right)$. To simplify this expression, we need to apply the distributive property and combine like terms.

Step 1: Apply the Distributive Property

The distributive property states that for any real numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$. We can apply this property to the first term, $2(p-4)$.

2(p-4) = 2p - 8

Step 2: Simplify the Second Term

The second term is $-\left(p^2+3p-6\right)$. We can simplify this term by distributing the negative sign to each term inside the parentheses.

-\left(p^2+3p-6\right) = -p^2 - 3p + 6

Step 3: Combine Like Terms

Now that we have simplified both terms, we can combine like terms to simplify the expression.

2p - 8 - p^2 - 3p + 6 = -p^2 + (2p - 3p) - 8 + 6

Step 4: Simplify the Expression

We can simplify the expression further by combining like terms.

-p^2 + (2p - 3p) - 8 + 6 = -p^2 - p - 2

Conclusion

In this article, we simplified the given expression: $2(p-4)-\left(p^2+3p-6\right)$. We applied the distributive property, combined like terms, and simplified the expression to get the final result: $-p^2 - p - 2$. This expression is now in its simplest form, and we can use it to solve equations and inequalities.

Tips and Tricks

• When simplifying expressions, always apply the distributive property to each term.
• Combine like terms to simplify the expression.
• Check your work by plugging in values to ensure that the expression is correct.

Common Mistakes

• Failing to apply the distributive property to each term.
• Not combining like terms to simplify the expression.
• Not checking the work by plugging in values.

Real-World Applications

Simplifying expressions is a crucial skill in algebra that has many real-world applications. For example, in physics, we use algebra to describe the motion of objects. In economics, we use algebra to model the behavior of markets. In computer science, we use algebra to write algorithms and solve problems.

Final Thoughts

Introduction

In our previous article, we simplified the expression: $2(p-4)-\left(p^2+3p-6\right)$. We applied the distributive property, combined like terms, and simplified the expression to get the final result: $-p^2 - p - 2$. In this article, we will answer some common questions related to simplifying expressions.

Q&A

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that states that for any real numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$. This property allows us to distribute a single term to multiple terms inside parentheses.

Q: How do I apply the distributive property?

A: To apply the distributive property, simply multiply the single term to each term inside the parentheses. For example, if we have the expression $2(p-4)$, we can apply the distributive property as follows:

2(p-4) = 2p - 8

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, $2p$ and $3p$ are like terms because they both have the variable $p$ raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, simply add or subtract the coefficients of the like terms. For example, if we have the expression $2p + 3p$, we can combine the like terms as follows:

2p + 3p = 5p

Q: What is the difference between a variable and a constant?

A: A variable is a letter or symbol that represents a value that can change. For example, $p$ is a variable. A constant is a value that does not change. For example, 2 is a constant.

Q: How do I simplify an expression with multiple variables?

A: To simplify an expression with multiple variables, simply apply the distributive property and combine like terms. For example, if we have the expression $2(p-4) - (p^2 + 3p - 6)$, we can simplify it as follows:

2(p-4) - (p^2 + 3p - 6) = -p^2 - p - 2

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

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

• Failing to apply the distributive property to each term.
• Not combining like terms to simplify the expression.
• Not checking the work by plugging in values.

Q: How do I check my work when simplifying expressions?

A: To check your work when simplifying expressions, simply plug in values to ensure that the expression is correct. For example, if we have the expression $-p^2 - p - 2$, we can plug in the value $p = 1$ to check that the expression is correct:

-p^2 - p - 2 = -(1)^2 - 1 - 2 = -4

Conclusion

Simplifying expressions is a fundamental skill in algebra that has many real-world applications. By applying the distributive property, combining like terms, and checking our work, we can simplify expressions and get the final result. Remember to always check your work by plugging in values to ensure that the expression is correct. With practice and patience, you will become proficient in simplifying expressions and solving equations and inequalities.

Tips and Tricks

• Always apply the distributive property to each term.
• Combine like terms to simplify the expression.
• Check your work by plugging in values.
• Use variables and constants correctly.
• Avoid common mistakes when simplifying expressions.

Real-World Applications

Simplifying expressions is a crucial skill in algebra that has many real-world applications. For example, in physics, we use algebra to describe the motion of objects. In economics, we use algebra to model the behavior of markets. In computer science, we use algebra to write algorithms and solve problems.

Final Thoughts

Simplifying expressions is a fundamental skill in algebra that helps us solve equations and inequalities. By applying the distributive property, combining like terms, and checking our work, we can simplify expressions and get the final result. Remember to always check your work by plugging in values to ensure that the expression is correct. With practice and patience, you will become proficient in simplifying expressions and solving equations and inequalities.