Multiply And Simplify Your Answer.\[$(6c - 5)(6c + 5)\$\]

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Introduction

In algebra, multiplying and simplifying expressions is a crucial skill that helps you solve equations and manipulate mathematical expressions. In this article, we will focus on multiplying and simplifying the expression $(6c - 5)(6c + 5)$. This type of problem is commonly encountered in algebra and is a great opportunity to practice your skills in expanding and simplifying expressions.

Understanding the Problem

The given expression is a product of two binomials, $(6c - 5)$ and $(6c + 5)$. To multiply these two binomials, 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 and then combine like terms.

Multiplying the Binomials

To multiply the binomials, we will start by multiplying each term in the first binomial by each term in the second binomial. This will result in four terms, which we will then combine like terms.

$(6c - 5)(6c + 5) = (6c)(6c) + (6c)(5) + (-5)(6c) + (-5)(5)$

Expanding the Terms

Now, let's expand each term in the expression.

$(6c)(6c) = 36c^2$

$(6c)(5) = 30c$

$(-5)(6c) = -30c$

$(-5)(5) = -25$

Combining Like Terms

Now that we have expanded each term, we can combine like terms. In this case, we have two terms with the variable $c$, $36c^2$ and $30c$, and two constant terms, $-25$ and $0$.

$36c^2 + 30c - 30c - 25$

Simplifying the Expression

Now, let's simplify the expression by combining like terms.

$36c^2 + 30c - 30c - 25 = 36c^2 - 25$

Conclusion

In this article, we multiplied and simplified the expression $(6c - 5)(6c + 5)$. We used the distributive property to multiply the binomials and then combined like terms to simplify the expression. The final answer is $36c^2 - 25$.

Tips and Tricks

• When multiplying binomials, make sure to use the distributive property to multiply each term in the first binomial by each term in the second binomial.
• When combining like terms, make sure to combine the coefficients of the variables and the constant terms separately.
• When simplifying expressions, make sure to combine like terms and eliminate any unnecessary terms.

Practice Problems

• Multiply and simplify the expression $(3x + 2)(3x - 2)$.
• Multiply and simplify the expression $(4y - 3)(4y + 3)$.
• Multiply and simplify the expression $(2z + 1)(2z - 1)$.

Real-World Applications

Multiplying and simplifying expressions is a crucial skill that has many real-world applications. For example, in physics, you may need to multiply and simplify expressions to solve problems involving motion and energy. In engineering, you may need to multiply and simplify expressions to design and analyze complex systems.

Conclusion

In conclusion, multiplying and simplifying expressions is a crucial skill that helps you solve equations and manipulate mathematical expressions. In this article, we multiplied and simplified the expression $(6c - 5)(6c + 5)$ and provided tips and tricks for multiplying and simplifying expressions. We also provided practice problems and real-world applications to help you understand the importance of this skill.

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Introduction

In our previous article, we multiplied and simplified the expression $(6c - 5)(6c + 5)$. In this article, we will answer some frequently asked questions about multiplying and simplifying expressions.

Q&A

Q: What is the distributive property?

A: The distributive property is a mathematical property that states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. This property is used to multiply binomials and trinomials.

Q: How do I multiply binomials?

A: To multiply binomials, you need to use the distributive property. Multiply each term in the first binomial by each term in the second binomial, and then combine like terms.

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, $2x$ and $3x$ are like terms because they both have the variable $x$ and the same exponent.

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the variables. For example, $2x + 3x = 5x$.

Q: What is the difference between multiplying and simplifying expressions?

A: Multiplying expressions involves multiplying two or more expressions together, while simplifying expressions involves combining like terms and eliminating any unnecessary terms.

Q: Can you give an example of multiplying and simplifying an expression?

A: Yes, let's multiply and simplify the expression $(3x + 2)(3x - 2)$. First, multiply the binomials using the distributive property:

$(3x + 2)(3x - 2) = (3x)(3x) + (3x)(-2) + (2)(3x) + (2)(-2)$

$= 9x^2 - 6x + 6x - 4$

$= 9x^2 - 4$

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

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

• Forgetting to use the distributive property when multiplying binomials
• Not combining like terms
• Not eliminating unnecessary terms
• Making errors when multiplying or adding numbers

Q: How can I practice multiplying and simplifying expressions?

A: You can practice multiplying and simplifying expressions by working through practice problems, such as those found in algebra textbooks or online resources. You can also try creating your own practice problems to challenge yourself.

Tips and Tricks

• Make sure to use the distributive property when multiplying binomials.
• Combine like terms carefully to avoid errors.
• Eliminate unnecessary terms to simplify the expression.
• Practice, practice, practice!

Conclusion

In conclusion, multiplying and simplifying expressions is a crucial skill that has many real-world applications. In this article, we answered some frequently asked questions about multiplying and simplifying expressions and provided tips and tricks for mastering this skill. We also provided examples and practice problems to help you understand the importance of this skill.

Practice Problems

• Multiply and simplify the expression $(4y - 3)(4y + 3)$.
• Multiply and simplify the expression $(2z + 1)(2z - 1)$.
• Multiply and simplify the expression $(3x + 2)(3x - 2)$.

Real-World Applications

Multiplying and simplifying expressions is a crucial skill that has many real-world applications. For example, in physics, you may need to multiply and simplify expressions to solve problems involving motion and energy. In engineering, you may need to multiply and simplify expressions to design and analyze complex systems.

Conclusion

In conclusion, multiplying and simplifying expressions is a crucial skill that helps you solve equations and manipulate mathematical expressions. In this article, we answered some frequently asked questions about multiplying and simplifying expressions and provided tips and tricks for mastering this skill. We also provided examples and practice problems to help you understand the importance of this skill.