Which Of The Following Is Equivalent To The Expression Below? { (p-4)(p+2)$}$A. { P^2 - 2p - 8$}$B. { P^2 - 4p - 2$}$C. { P^2 - 8$}$D. { P^2 - 2$}$

Introduction

Algebraic expressions are a fundamental concept in mathematics, and understanding how to solve them is crucial for success in various mathematical disciplines. In this article, we will focus on solving a specific type of algebraic expression, namely the multiplication of two binomials. We will use the given expression $(p-4)(p+2)$ as an example and explore the different methods to simplify it.

Understanding the Expression

The given expression is a product of two binomials, $(p-4)$ and $(p+2)$. To simplify this expression, we need to apply the distributive property, which states that for any real numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$. We will use this property to expand the given expression.

Expanding the Expression

To expand the expression $(p-4)(p+2)$, we need to multiply each term in the first binomial by each term in the second binomial. This can be done using the distributive property:

$(p-4)(p+2) = p(p+2) - 4(p+2)$

Now, we can simplify each term separately:

$p(p+2) = p^2 + 2p$

$-4(p+2) = -4p - 8$

Combining these two terms, we get:

$(p-4)(p+2) = p^2 + 2p - 4p - 8$

Simplifying further, we get:

$(p-4)(p+2) = p^2 - 2p - 8$

Comparing with the Options

Now that we have simplified the expression $(p-4)(p+2)$, we can compare it with the given options:

A. $p^2 - 2p - 8$ B. $p^2 - 4p - 2$ C. $p^2 - 8$ D. $p^2 - 2$

From the simplified expression, we can see that the correct answer is:

A. $p^2 - 2p - 8$

Conclusion

In this article, we have explored the process of simplifying an algebraic expression using the distributive property. We have used the given expression $(p-4)(p+2)$ as an example and simplified it step by step. We have also compared the simplified expression with the given options and identified the correct answer. This article provides a clear and concise guide to solving algebraic expressions, making it an essential resource for students and educators alike.

Frequently Asked Questions

Q: What is the distributive property?

A: The distributive property is a mathematical concept that states that for any real numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$.

Q: How do I simplify an algebraic expression using the distributive property?

A: To simplify an algebraic expression using the distributive property, you need to multiply each term in the first binomial by each term in the second binomial and then combine like terms.

Q: What is the correct answer to the given expression $(p-4)(p+2)$?

A: The correct answer to the given expression $(p-4)(p+2)$ is $p^2 - 2p - 8$.

Additional Resources

For more information on algebraic expressions and the distributive property, please refer to the following resources:

• Khan Academy: Algebraic Expressions
• Mathway: Distributive Property
• Wolfram Alpha: Algebraic Expressions

References

• "Algebra" by Michael Artin
• "Calculus" by Michael Spivak
• "Mathematics for Computer Science" by Eric Lehman and Tom Leighton
  Algebraic Expressions Q&A: A Comprehensive Guide =====================================================

Introduction

Algebraic expressions are a fundamental concept in mathematics, and understanding how to work with them is crucial for success in various mathematical disciplines. In this article, we will provide a comprehensive Q&A guide to algebraic expressions, covering topics such as simplifying expressions, factoring, and solving equations.

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to combine like terms, which involves adding or subtracting terms that have the same variable and exponent. For example, $2x + 3x$ can be simplified to $5x$.

Q: What is the distributive property?

A: The distributive property is a mathematical concept that states that for any real numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$. This property allows you to expand expressions by multiplying each term in the first binomial by each term in the second binomial.

Q: How do I factor an algebraic expression?

A: Factoring an algebraic expression involves expressing it as a product of simpler expressions. For example, $6x + 12$ can be factored as $6(x+2)$.

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

A: A variable is a symbol that represents a value that can change, while a constant is a value that remains the same.

Q: How do I solve an equation with variables?

A: To solve an equation with variables, you need to isolate the variable by performing operations that eliminate the constant term. For example, to solve the equation $2x + 3 = 5$, you would subtract 3 from both sides to get $2x = 2$, and then divide both sides by 2 to get $x = 1$.

Q: What is the order of operations?

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 evaluate an expression with multiple operations?

A: To evaluate an expression with multiple operations, you need to follow the order of operations. For example, to evaluate the expression $3 + 2 \times 4$, you would first multiply 2 and 4 to get 8, and then add 3 to get 11.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable is 1, while a quadratic equation is an equation in which the highest power of the variable is 2.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you can use the quadratic formula, which is:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

where $a$, $b$, and $c$ are the coefficients of the quadratic equation.

Conclusion

In this article, we have provided a comprehensive Q&A guide to algebraic expressions, covering topics such as simplifying expressions, factoring, and solving equations. We hope that this guide has been helpful in answering your questions and providing a better understanding of algebraic expressions.

Additional Resources

For more information on algebraic expressions and the topics covered in this article, please refer to the following resources:

• Khan Academy: Algebraic Expressions
• Mathway: Algebraic Expressions
• Wolfram Alpha: Algebraic Expressions

References

• "Algebra" by Michael Artin
• "Calculus" by Michael Spivak
• "Mathematics for Computer Science" by Eric Lehman and Tom Leighton