Expand And Collect Like Terms: { (7 + 6d)(7 - 6d)$} A N S W E R : Answer: A N S W Er : { (7 + 6d)(7 - 6d) =\$}

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Introduction

In algebra, expanding and collecting like terms is a crucial step in simplifying expressions and solving equations. It involves multiplying out the terms in an expression and combining like terms to obtain a simpler form. In this article, we will focus on expanding and collecting like terms in the expression $(7 + 6d)(7 - 6d)$.

Understanding the Expression

The given expression is a product of two binomials, $(7 + 6d)$ and $(7 - 6d)$. To expand and collect like terms, we need to multiply each term in the first binomial by each term in the second binomial.

Expanding the Expression

To expand the expression, we will use the distributive property, which states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. We will apply this property to each term in the first binomial.

$(7 + 6d)(7 - 6d) = 7(7 - 6d) + 6d(7 - 6d)$

Multiplying Out the Terms

Now, we will multiply out the terms in each binomial.

$7(7 - 6d) = 49 - 42d$

$6d(7 - 6d) = 42d - 36d^2$

Combining Like Terms

Now, we will combine like terms by adding or subtracting the coefficients of the same variables.

$(49 - 42d) + (42d - 36d^2) = 49 - 36d^2$

Final Answer

Therefore, the expanded and simplified form of the expression $(7 + 6d)(7 - 6d)$ is $49 - 36d^2$.

Conclusion

In this article, we have expanded and collected like terms in the expression $(7 + 6d)(7 - 6d)$. We have used the distributive property to multiply out the terms in each binomial and then combined like terms to obtain the simplified form of the expression. This process is an essential step in simplifying expressions and solving equations in algebra.

Tips and Tricks

• When expanding and collecting like terms, make sure to multiply out all the terms in each binomial.
• Use the distributive property to simplify the expression.
• Combine like terms by adding or subtracting the coefficients of the same variables.
• Check your work by plugging in values for the variables to ensure that the expression is true.

Real-World Applications

Expanding and collecting like terms has many real-world applications in fields such as physics, engineering, and economics. For example, in physics, the expression $(7 + 6d)(7 - 6d)$ can be used to represent the area of a rectangle with a length of $7$ and a width of $7 - 6d$. In engineering, the expression can be used to represent the volume of a cylinder with a radius of $7$ and a height of $7 - 6d$. In economics, the expression can be used to represent the profit of a company with a revenue of $7$ and a cost of $7 - 6d$.

Common Mistakes

• Failing to multiply out all the terms in each binomial.
• Failing to combine like terms.
• Making errors when simplifying the expression.

Final Thoughts

Expanding and collecting like terms is an essential skill in algebra that has many real-world applications. By following the steps outlined in this article, you can simplify expressions and solve equations with ease. Remember to always multiply out all the terms in each binomial and combine like terms to obtain the simplified form of the expression.

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Introduction

In our previous article, we expanded and collected like terms in the expression $(7 + 6d)(7 - 6d)$. In this article, we will answer some frequently asked questions about expanding and collecting like terms.

Q&A

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 is used to multiply out the terms in an expression.

Q: How do I expand an expression with two binomials?

A: To expand an expression with two binomials, you need to multiply each term in the first binomial by each term in the second binomial. You can use the distributive property to simplify the expression.

Q: What is the difference between expanding and collecting like terms?

A: Expanding an expression involves multiplying out the terms in the expression, while collecting like terms involves combining the terms with the same variables.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the same variables. For example, if you have the expression $2x + 3x$, you can combine the like terms by adding the coefficients: $2x + 3x = 5x$.

Q: What are some common mistakes to avoid when expanding and collecting like terms?

A: Some common mistakes to avoid when expanding and collecting like terms include:

• Failing to multiply out all the terms in each binomial
• Failing to combine like terms
• Making errors when simplifying the expression

Q: How do I check my work when expanding and collecting like terms?

A: To check your work, you can plug in values for the variables to ensure that the expression is true. For example, if you have the expression $x^2 + 4x + 4$, you can plug in $x = 0$ to check that the expression is true.

Q: What are some real-world applications of expanding and collecting like terms?

A: Expanding and collecting like terms has many real-world applications in fields such as physics, engineering, and economics. For example, in physics, the expression $(7 + 6d)(7 - 6d)$ can be used to represent the area of a rectangle with a length of $7$ and a width of $7 - 6d$.

Q: How can I practice expanding and collecting like terms?

A: You can practice expanding and collecting like terms by working through exercises and problems in your textbook or online resources. You can also try creating your own expressions and simplifying them to practice your skills.

Conclusion

Expanding and collecting like terms is an essential skill in algebra that has many real-world applications. By following the steps outlined in this article, you can simplify expressions and solve equations with ease. Remember to always multiply out all the terms in each binomial and combine like terms to obtain the simplified form of the expression.

Tips and Tricks

• Practice, practice, practice: The more you practice expanding and collecting like terms, the more comfortable you will become with the process.
• Use online resources: There are many online resources available that can help you practice expanding and collecting like terms, such as Khan Academy and Mathway.
• Work with a partner: Working with a partner can help you stay motivated and get help when you need it.
• Take your time: Expanding and collecting like terms can be a complex process, so take your time and make sure you understand each step before moving on.

Final Thoughts

Expanding and collecting like terms is an essential skill in algebra that has many real-world applications. By following the steps outlined in this article and practicing regularly, you can simplify expressions and solve equations with ease. Remember to always multiply out all the terms in each binomial and combine like terms to obtain the simplified form of the expression.