Expand The Expression: 5 X 2 ( X − 8 5x^2(x-8 5 X 2 ( X − 8 ]A. 5 X 3 − 8 X 2 5x^3 - 8x^2 5 X 3 − 8 X 2 B. 5 X 2 − 8 X 2 5x^2 - 8x^2 5 X 2 − 8 X 2 C. 5 X 3 − 40 5x^3 - 40 5 X 3 − 40 D. 5 X 3 − 13 5x^3 - 13 5 X 3 − 13

Introduction

Algebraic expressions are a fundamental concept in mathematics, and expanding them is a crucial skill to master. In this article, we will focus on expanding the expression $5x^2(x-8)$, which is a common problem in algebra. We will break down the steps involved in expanding this expression and provide a clear explanation of each step.

Understanding the Expression

Before we start expanding the expression, let's understand what it means. The expression $5x^2(x-8)$ is a product of two binomials: $5x^2$ and $(x-8)$. To expand this expression, we need to multiply each term in the first binomial by each term in the second binomial.

Step 1: Multiply Each Term in the First Binomial by Each Term in the Second Binomial

To expand the expression, we need to multiply each term in the first binomial ($5x^2$) by each term in the second binomial ($x-8$). We can start by multiplying $5x^2$ by $x$ and then by $-8$.

Multiplying $5x^2$ by $x$

When we multiply $5x^2$ by $x$, we need to multiply the coefficient ($5$) by the variable ($x$) and then multiply the exponent ($2$) by the variable ($x$). This gives us $5x^3$.

Multiplying $5x^2$ by $-8$

When we multiply $5x^2$ by $-8$, we need to multiply the coefficient ($5$) by the constant ($-8$) and then multiply the exponent ($2$) by the constant ($-8$). This gives us $-40x^2$.

Step 2: Combine Like Terms

Now that we have multiplied each term in the first binomial by each term in the second binomial, we can combine like terms. In this case, we have two terms: $5x^3$ and $-40x^2$. We can combine these terms by adding or subtracting them.

Combining $5x^3$ and $-40x^2$

When we combine $5x^3$ and $-40x^2$, we get $5x^3 - 40x^2$.

Conclusion

In conclusion, expanding the expression $5x^2(x-8)$ involves multiplying each term in the first binomial by each term in the second binomial and then combining like terms. By following these steps, we can expand the expression and simplify it to $5x^3 - 40x^2$.

Answer

The correct answer is C. $5x^3 - 40$.

Why is this the correct answer?

This is the correct answer because when we multiply $5x^2$ by $x$, we get $5x^3$, and when we multiply $5x^2$ by $-8$, we get $-40x^2$. Therefore, the correct expansion of the expression is $5x^3 - 40x^2$.

Common Mistakes

When expanding algebraic expressions, it's easy to make mistakes. Here are some common mistakes to avoid:

• Not multiplying each term in the first binomial by each term in the second binomial: This is a common mistake that can lead to incorrect expansions.
• Not combining like terms: This can also lead to incorrect expansions.
• Not following the order of operations: This can also lead to incorrect expansions.

Tips and Tricks

Here are some tips and tricks to help you expand algebraic expressions:

• Use the distributive property: This property states that a(b+c) = ab + ac. This can help you expand expressions by multiplying each term in the first binomial by each term in the second binomial.
• Combine like terms: This can help you simplify expressions and make them easier to work with.
• Follow the order of operations: This can help you avoid mistakes and ensure that you're expanding expressions correctly.

Conclusion

Introduction

In our previous article, we discussed how to expand algebraic expressions using the distributive property. In this article, we will provide a Q&A guide to help you understand the concept better and answer some common questions.

Q: What is the distributive property?

A: The distributive property is a mathematical concept that states that a(b+c) = ab + ac. This means that when you multiply a single term by two or more terms, you can multiply each term separately and then add them together.

Q: How do I apply the distributive property to expand an expression?

A: To apply the distributive property, you need to multiply each term in the first binomial by each term in the second binomial. For example, if you have the expression 2(x+3), you would multiply 2 by x and then multiply 2 by 3.

Q: What is the difference between expanding and simplifying an expression?

A: Expanding an expression means multiplying each term in the first binomial by each term in the second binomial, while simplifying an expression means combining like terms to make it easier to work with.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract terms that have the same variable and exponent. For example, if you have the expression 2x + 3x, you would combine the two terms to get 5x.

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

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

• Not multiplying each term in the first binomial by each term in the second binomial
• Not combining like terms
• Not following the order of operations

Q: How do I use the distributive property to expand expressions with exponents?

A: To use the distributive property to expand expressions with exponents, you need to multiply each term in the first binomial by each term in the second binomial, taking into account the exponents. For example, if you have the expression 2x^2(x+3), you would multiply 2x^2 by x and then multiply 2x^2 by 3.

Q: Can I use the distributive property to expand expressions with fractions?

A: Yes, you can use the distributive property to expand expressions with fractions. However, you need to be careful when multiplying fractions, as you need to multiply the numerators and denominators separately.

Q: How do I simplify expressions with fractions?

A: To simplify expressions with fractions, you need to combine like terms and then simplify the fraction. For example, if you have the expression 2x/3 + 3x/3, you would combine the two terms to get 5x/3.

Q: What are some real-world applications of expanding and simplifying expressions?

A: Expanding and simplifying expressions have many real-world applications, including:

• Algebra: Expanding and simplifying expressions are essential skills in algebra, as they help you solve equations and inequalities.
• Calculus: Expanding and simplifying expressions are also essential skills in calculus, as they help you find derivatives and integrals.
• Physics: Expanding and simplifying expressions are used in physics to describe the motion of objects and the behavior of physical systems.
• Engineering: Expanding and simplifying expressions are used in engineering to design and optimize systems.

Conclusion

In conclusion, expanding and simplifying expressions are essential skills in mathematics, with many real-world applications. By understanding the distributive property and how to apply it, you can expand and simplify expressions with ease. Remember to be careful when multiplying fractions and to combine like terms to simplify expressions.