Find The Square And Simplify Your Answer.$(3s - 3)^2$

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Understanding the Problem

When dealing with algebraic expressions, one common operation is squaring a binomial. In this case, we are given the expression $(3s - 3)^2$ and asked to find the square and simplify our answer. To approach this problem, we need to understand the concept of squaring a binomial and how to apply the formula.

Squaring a Binomial

A binomial is an algebraic expression consisting of two terms. When we square a binomial, we are essentially multiplying the expression by itself. The formula for squaring a binomial is:

$(a + b)^2 = a^2 + 2ab + b^2$

$(a - b)^2 = a^2 - 2ab + b^2$

In our given expression, $(3s - 3)^2$, we can see that it is in the form of $(a - b)^2$, where $a = 3s$ and $b = 3$.

Applying the Formula

Now that we have identified the form of the expression, we can apply the formula to find the square.

$(3s - 3)^2 = (3s)^2 - 2(3s)(3) + 3^2$

Expanding the Terms

To simplify the expression, we need to expand the terms.

$(3s)^2 = 9s^2$

$-2(3s)(3) = -18s$

$3^2 = 9$

Combining the Terms

Now that we have expanded the terms, we can combine them to simplify the expression.

$(3s - 3)^2 = 9s^2 - 18s + 9$

Simplifying the Expression

The expression $9s^2 - 18s + 9$ is already simplified, but we can further simplify it by factoring out the greatest common factor (GCF).

Factoring Out the GCF

The GCF of the terms $9s^2$, $-18s$, and $9$ is $9$. We can factor out the GCF to simplify the expression.

$9s^2 - 18s + 9 = 9(s^2 - 2s + 1)$

Final Answer

The final answer to the problem is $9(s^2 - 2s + 1)$.

Conclusion

In this article, we have learned how to find the square and simplify the expression $(3s - 3)^2$. We applied the formula for squaring a binomial, expanded the terms, combined them, and simplified the expression by factoring out the greatest common factor. The final answer is $9(s^2 - 2s + 1)$.

Frequently Asked Questions

• What is the formula for squaring a binomial? The formula for squaring a binomial is $(a + b)^2 = a^2 + 2ab + b^2$ and $(a - b)^2 = a^2 - 2ab + b^2$.
• How do I apply the formula to find the square? To apply the formula, identify the form of the expression and substitute the values of $a$ and $b$ into the formula.
• How do I simplify the expression? To simplify the expression, expand the terms, combine them, and factor out the greatest common factor.

Additional Resources

• Algebraic Expressions: A Comprehensive Guide
• Squaring a Binomial: A Step-by-Step Guide
• Simplifying Algebraic Expressions: Tips and Tricks
  

Understanding the Basics

Squaring a binomial is a fundamental concept in algebra that can be used to simplify complex expressions. In this article, we will answer some of the most frequently asked questions about squaring a binomial.

Q: What is a binomial?

A: A binomial is an algebraic expression consisting of two terms. It can be in the form of $(a + b)$ or $(a - b)$.

Q: What is the formula for squaring a binomial?

A: The formula for squaring a binomial is:

$(a + b)^2 = a^2 + 2ab + b^2$

$(a - b)^2 = a^2 - 2ab + b^2$

Q: How do I apply the formula to find the square?

A: To apply the formula, identify the form of the expression and substitute the values of $a$ and $b$ into the formula. For example, if we have the expression $(3s - 3)^2$, we can see that it is in the form of $(a - b)^2$, where $a = 3s$ and $b = 3$.

Q: What is the difference between $(a + b)^2$ and $(a - b)^2$?

A: The main difference between $(a + b)^2$ and $(a - b)^2$ is the sign of the middle term. In $(a + b)^2$, the middle term is $2ab$, while in $(a - b)^2$, the middle term is $-2ab$.

Q: How do I simplify the expression after squaring a binomial?

A: To simplify the expression, expand the terms, combine them, and factor out the greatest common factor (GCF). For example, if we have the expression $(3s - 3)^2 = 9s^2 - 18s + 9$, we can simplify it by factoring out the GCF, which is $9$.

Q: What is the greatest common factor (GCF)?

A: The greatest common factor (GCF) is the largest factor that divides all the terms of an expression. In the expression $9s^2 - 18s + 9$, the GCF is $9$.

Q: How do I factor out the GCF?

A: To factor out the GCF, divide each term of the expression by the GCF. For example, in the expression $9s^2 - 18s + 9$, we can factor out the GCF by dividing each term by $9$, resulting in $s^2 - 2s + 1$.

Q: What is the final answer to the problem?

A: The final answer to the problem is the simplified expression after squaring a binomial and factoring out the GCF.

Q: Can I use the formula for squaring a binomial to simplify complex expressions?

A: Yes, the formula for squaring a binomial can be used to simplify complex expressions. However, it is essential to identify the form of the expression and apply the correct formula.

Q: What are some common mistakes to avoid when squaring a binomial?

A: Some common mistakes to avoid when squaring a binomial include:

• Not identifying the form of the expression
• Not applying the correct formula
• Not factoring out the GCF
• Not simplifying the expression

Q: How can I practice squaring a binomial?

A: You can practice squaring a binomial by working through examples and exercises. Start with simple expressions and gradually move on to more complex ones.

Q: What are some real-world applications of squaring a binomial?

A: Squaring a binomial has many real-world applications, including:

• Calculating the area of a rectangle
• Finding the volume of a cube
• Determining the distance between two points
• Solving problems in physics and engineering

Conclusion

Squaring a binomial is a fundamental concept in algebra that can be used to simplify complex expressions. By understanding the basics of squaring a binomial, you can apply the formula to find the square and simplify the expression. Remember to identify the form of the expression, apply the correct formula, and factor out the greatest common factor to get the final answer.