Expand $9k(k-2)$.

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Introduction

In algebra, expanding an expression involves multiplying the terms within the expression to simplify it. The expression $9k(k-2)$ is a quadratic expression that can be expanded using the distributive property. In this article, we will learn how to expand the given expression and understand the concept behind it.

Understanding the Expression

The given expression is $9k(k-2)$. This expression consists of two terms: $9k$ and $(k-2)$. To expand this expression, we need to multiply the two terms using the distributive property.

Applying the Distributive Property

The distributive property states that for any real numbers $a$, $b$, and $c$, the following equation holds:

a(b+c)=ab+aca(b+c) = ab + ac

Using this property, we can expand the given expression as follows:

9k(k−2)=9k⋅k−9k⋅29k(k-2) = 9k \cdot k - 9k \cdot 2

Multiplying the Terms

Now, we need to multiply the terms within the expression. We can start by multiplying $9k$ with $k$:

9kâ‹…k=9k29k \cdot k = 9k^2

Next, we multiply $9k$ with $-2$:

9k⋅−2=−18k9k \cdot -2 = -18k

Combining the Terms

Now that we have multiplied the terms, we can combine them to get the final expanded expression:

9k(k−2)=9k2−18k9k(k-2) = 9k^2 - 18k

Simplifying the Expression

The expanded expression $9k^2 - 18k$ can be simplified further by factoring out the common term $9k$:

9k2−18k=9k(k−2)9k^2 - 18k = 9k(k-2)

Conclusion

In this article, we learned how to expand the algebraic expression $9k(k-2)$ using the distributive property. We applied the distributive property to multiply the terms within the expression and obtained the final expanded expression $9k^2 - 18k$. We also simplified the expression by factoring out the common term $9k$. This example demonstrates the importance of understanding the distributive property and how it can be used to simplify algebraic expressions.

Real-World Applications

The concept of expanding algebraic expressions has numerous real-world applications. For example, in physics, the expansion of expressions is used to describe the motion of objects. In engineering, it is used to design and analyze complex systems. In economics, it is used to model and analyze economic systems.

Tips and Tricks

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

  • Use the distributive property to multiply the terms within the expression.
  • Simplify the expression by factoring out common terms.
  • Use algebraic identities to simplify the expression.
  • Check your work by plugging in values for the variables.

Practice Problems

Here are some practice problems to help you practice expanding algebraic expressions:

  • Expand the expression $4x(x+3)$.
  • Expand the expression $2y(y-4)$.
  • Expand the expression $3z(z+2)$.

Answer Key

Here are the answers to the practice problems:

  • 4x(x+3)=4x2+12x4x(x+3) = 4x^2 + 12x

  • 2y(y−4)=2y2−8y2y(y-4) = 2y^2 - 8y

  • 3z(z+2)=3z2+6z3z(z+2) = 3z^2 + 6z

Conclusion

Introduction

In our previous article, we learned how to expand the algebraic expression $9k(k-2)$ using the distributive property. In this article, we will provide a Q&A guide to help you understand the concept of expanding algebraic expressions and address any questions you may have.

Q: What is the distributive property?

A: The distributive property is a mathematical concept that states that for any real numbers $a$, $b$, and $c$, the following equation holds:

a(b+c)=ab+aca(b+c) = ab + ac

This property allows us to multiply the terms within an expression and simplify it.

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

A: To apply the distributive property, you need to multiply the terms within the expression using the following steps:

  1. Multiply the first term with the second term.
  2. Multiply the first term with the third term.
  3. Combine the terms to get the final expanded expression.

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

A: Here are some common mistakes to avoid when expanding expressions:

  • Not using the distributive property correctly.
  • Not multiplying the terms within the expression.
  • Not combining the terms correctly.
  • Not simplifying the expression.

Q: How do I simplify an expression after expanding it?

A: To simplify an expression after expanding it, you can use the following steps:

  1. Factor out common terms.
  2. Combine like terms.
  3. Simplify the expression using algebraic identities.

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

A: Expanding algebraic expressions has numerous real-world applications, including:

  • Physics: to describe the motion of objects.
  • Engineering: to design and analyze complex systems.
  • Economics: to model and analyze economic systems.

Q: How can I practice expanding algebraic expressions?

A: Here are some ways to practice expanding algebraic expressions:

  • Use online resources and practice problems.
  • Work with a tutor or teacher.
  • Practice with real-world examples.

Q: What are some tips and tricks to help me expand algebraic expressions?

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

  • Use the distributive property to multiply the terms within the expression.
  • Simplify the expression by factoring out common terms.
  • Use algebraic identities to simplify the expression.
  • Check your work by plugging in values for the variables.

Q: How can I use algebraic expressions in real-world problems?

A: Algebraic expressions can be used to model and analyze real-world problems, including:

  • Physics: to describe the motion of objects.
  • Engineering: to design and analyze complex systems.
  • Economics: to model and analyze economic systems.

Conclusion

In conclusion, expanding algebraic expressions is an important concept in algebra that has numerous real-world applications. By understanding the distributive property and how to apply it, you can simplify complex expressions and solve problems in various fields. Remember to practice regularly and use the tips and tricks provided to help you expand algebraic expressions with ease.

Practice Problems

Here are some practice problems to help you practice expanding algebraic expressions:

  • Expand the expression $4x(x+3)$.
  • Expand the expression $2y(y-4)$.
  • Expand the expression $3z(z+2)$.

Answer Key

Here are the answers to the practice problems:

  • 4x(x+3)=4x2+12x4x(x+3) = 4x^2 + 12x

  • 2y(y−4)=2y2−8y2y(y-4) = 2y^2 - 8y

  • 3z(z+2)=3z2+6z3z(z+2) = 3z^2 + 6z

Additional Resources

Here are some additional resources to help you learn more about expanding algebraic expressions:

  • Online resources: Khan Academy, Mathway, and Wolfram Alpha.
  • Textbooks: Algebra by Michael Artin and Algebra by David S. Dummit.
  • Tutors and teachers: work with a tutor or teacher to get personalized help.

Conclusion

In conclusion, expanding algebraic expressions is an important concept in algebra that has numerous real-world applications. By understanding the distributive property and how to apply it, you can simplify complex expressions and solve problems in various fields. Remember to practice regularly and use the tips and tricks provided to help you expand algebraic expressions with ease.