Which Shows $23^2-17^2$ Being Evaluated Using The Difference Of Perfect Squares Method?A. $23^2-17^2=(529+289)(529-289)=196,320$B. \$23^2-17^2=529-289=240$[/tex\]C. $23^2-17^2=(23+17)(23-17)=(40)(6)=240$D.

Feb 26, 2025 by ADMIN 213 views

**Evaluating Expressions Using the Difference of Perfect Squares Method**

Introduction

In algebra, the difference of perfect squares method is a technique used to simplify expressions of the form $a^2 - b^2$ . This method involves factoring the expression into the product of two binomials, which can then be simplified further. In this article, we will explore how to evaluate expressions using the difference of perfect squares method, with a focus on the given problem: $23^2 - 17^2$ .

The Difference of Perfect Squares Method

The difference of perfect squares method is based on the following formula:

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

This formula can be derived by multiplying the expression $a^2 - b^2$ by the conjugate of the binomial $a + b$ , which is $a - b$ . The result is:

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

Applying the Difference of Perfect Squares Method

Now, let's apply the difference of perfect squares method to the given problem: $23^2 - 17^2$ . We can start by identifying the values of $a$ and $b$ :

$a = 23$ $b = 17$

Using the formula, we can write:

$23^2 - 17^2 = (23 + 17)(23 - 17)$

Evaluating the Expression

Now, we can evaluate the expression by multiplying the two binomials:

$(23 + 17)(23 - 17) = (40)(6)$

Simplifying the Expression

Finally, we can simplify the expression by multiplying the two numbers:

$(40)(6) = 240$

Conclusion

In this article, we have explored how to evaluate expressions using the difference of perfect squares method. We have applied this method to the given problem: $23^2 - 17^2$ , and have shown that the correct answer is:

$23^2 - 17^2 = (23 + 17)(23 - 17) = (40)(6) = 240$

Comparison of Options

Let's compare the options given in the problem:

A. $23^2 - 17^2 = (529 + 289)(529 - 289) = 196,320$

This option is incorrect, as it does not follow the difference of perfect squares method.

B. $23^2 - 17^2 = 529 - 289 = 240$

This option is incorrect, as it does not follow the difference of perfect squares method.

C. $23^2 - 17^2 = (23 + 17)(23 - 17) = (40)(6) = 240$

This option is correct, as it follows the difference of perfect squares method.

D. (no option provided)

Discussion

The difference of perfect squares method is a powerful tool for simplifying expressions of the form $a^2 - b^2$ . By applying this method, we can simplify complex expressions and arrive at the correct answer. In this article, we have shown how to evaluate expressions using the difference of perfect squares method, with a focus on the given problem: $23^2 - 17^2$ .

Key Takeaways

The difference of perfect squares method is a technique used to simplify expressions of the form $a^2 - b^2$ .
The formula for the difference of perfect squares method is: $a^2 - b^2 = (a + b)(a - b)$ .
By applying the difference of perfect squares method, we can simplify complex expressions and arrive at the correct answer.

References

[1] "Algebra" by Michael Artin
[2] "Calculus" by Michael Spivak

Additional Resources

Khan Academy: Algebra
MIT OpenCourseWare: Algebra
Wolfram Alpha: Algebra
Frequently Asked Questions (FAQs) About the Difference of Perfect Squares Method ====================================================================================

Introduction

In our previous article, we explored the difference of perfect squares method, a technique used to simplify expressions of the form $a^2 - b^2$ . In this article, we will answer some frequently asked questions (FAQs) about the difference of perfect squares method.

Q: What is the difference of perfect squares method?

A: The difference of perfect squares method is a technique used to simplify expressions of the form $a^2 - b^2$ . It involves factoring the expression into the product of two binomials, which can then be simplified further.

Q: How do I apply the difference of perfect squares method?

A: To apply the difference of perfect squares method, you need to identify the values of $a$ and $b$ in the expression $a^2 - b^2$ . Then, you can use the formula: $a^2 - b^2 = (a + b)(a - b)$ to factor the expression.

Q: What is the formula for the difference of perfect squares method?

A: The formula for the difference of perfect squares method is: $a^2 - b^2 = (a + b)(a - b)$ .

Q: Can I use the difference of perfect squares method with any expression?

A: No, the difference of perfect squares method can only be used with expressions of the form $a^2 - b^2$ . If the expression is not in this form, you cannot use the difference of perfect squares method.

Q: How do I simplify the expression after applying the difference of perfect squares method?

A: After applying the difference of perfect squares method, you can simplify the expression by multiplying the two binomials. For example, if you have the expression $(a + b)(a - b)$ , you can simplify it by multiplying the two binomials: $(a + b)(a - b) = a^2 - b^2$ .

Q: What are some common mistakes to avoid when using the difference of perfect squares method?

A: Some common mistakes to avoid when using the difference of perfect squares method include:

Not identifying the values of $a$ and $b$ correctly
Not using the correct formula: $a^2 - b^2 = (a + b)(a - b)$
Not simplifying the expression correctly after applying the difference of perfect squares method

Q: Can I use the difference of perfect squares method with negative numbers?

A: Yes, you can use the difference of perfect squares method with negative numbers. For example, if you have the expression $(-a)^2 - b^2$ , you can apply the difference of perfect squares method by identifying the values of $a$ and $b$ and using the formula: $(-a)^2 - b^2 = (a + b)(a - b)$ .

Q: How do I know if the difference of perfect squares method is the correct method to use?

A: To determine if the difference of perfect squares method is the correct method to use, you need to check if the expression is in the form $a^2 - b^2$ . If it is, then the difference of perfect squares method is the correct method to use.

Conclusion

In this article, we have answered some frequently asked questions (FAQs) about the difference of perfect squares method. We hope that this article has been helpful in clarifying any doubts you may have had about the difference of perfect squares method.

Key Takeaways

The difference of perfect squares method is a technique used to simplify expressions of the form $a^2 - b^2$ .
The formula for the difference of perfect squares method is: $a^2 - b^2 = (a + b)(a - b)$ .
You can use the difference of perfect squares method with negative numbers.
You need to identify the values of $a$ and $b$ correctly and use the correct formula to apply the difference of perfect squares method.

References

[1] "Algebra" by Michael Artin
[2] "Calculus" by Michael Spivak

Additional Resources

Khan Academy: Algebra
MIT OpenCourseWare: Algebra
Wolfram Alpha: Algebra