Which Expression Is Equivalent To $100 N^2-1$?A. $(10 N) 2-(1) 2$ B. $\left(10 N 2\right) 2-(1)^2$ C. $ ( 50 N ) 2 − ( 1 ) 2 (50 N)^2-(1)^2 ( 50 N ) 2 − ( 1 ) 2 [/tex] D. $\left(50 N 2\right) 2-(1)^2$

Mar 10, 2025 by ADMIN 212 views

**Which Expression is Equivalent to $100 n^2-1$?**

Introduction

In mathematics, algebraic expressions are used to represent various mathematical operations and relationships. One of the fundamental concepts in algebra is the difference of squares, which is a common technique used to simplify and manipulate expressions. In this article, we will explore the concept of difference of squares and apply it to find the equivalent expression for $100 n^2-1$ .

Understanding the Difference of Squares

The difference of squares is a mathematical formula that states:

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

This formula can be used to simplify expressions that involve the subtraction of two squares. To apply this formula, we need to identify the two squares and then factor them using the difference of squares formula.

Applying the Difference of Squares Formula

Let's apply the difference of squares formula to the given expression $100 n^2-1$ . We can rewrite $100 n^2$ as $(10 n)^2$ and $1$ as $(1)^2$ . Now, we can use the difference of squares formula to simplify the expression:

100 n^2-1 = (10 n)^2-(1)^2

This expression is equivalent to the difference of squares formula, where $a = 10 n$ and $b = 1$ .

Evaluating the Options

Now, let's evaluate the given options to determine which one is equivalent to $100 n^2-1$ .

Option A: $(10 n)^2-(1)2$

As we have already shown, this expression is equivalent to $100 n^2-1$ .

Option B: $\left(10 n^2\right)2-(1)^2$

This expression is not equivalent to $100 n^2-1$ because it involves squaring $10 n^2$ , which is not the same as squaring $10 n$ .

Option C: $(50 n)^2-(1)2$

This expression is not equivalent to $100 n^2-1$ because it involves squaring $50 n$ , which is not the same as squaring $10 n$ .

Option D: $\left(50 n^2\right)2-(1)^2$

This expression is not equivalent to $100 n^2-1$ because it involves squaring $50 n^2$ , which is not the same as squaring $10 n$ .

Conclusion

In conclusion, the expression that is equivalent to $100 n^2-1$ is:

(10 n)^2-(1)^2

This expression can be simplified using the difference of squares formula, which states that $a^2 - b^2 = (a + b)(a - b)$ . By applying this formula, we can simplify the expression and find its equivalent form.

Final Answer

The final answer is:

(10 n)^2-(1)^2$<br/> **Q&A: Which Expression is Equivalent to $100 n^2-1$?** =====================================================

Introduction

In our previous article, we explored the concept of difference of squares and applied it to find the equivalent expression for $100 n^2-1$ . We also evaluated the given options to determine which one is equivalent to $100 n^2-1$ . In this article, we will provide a Q&A section to further clarify any doubts and provide additional information on the topic.

Q: What is the difference of squares formula?

A: The difference of squares formula is a mathematical formula that states:

Introduction

Understanding the Difference of Squares

Applying the Difference of Squares Formula

Evaluating the Options

Option A: $(10 n)2-(1)2$

Option B: $\left(10 n2\right)2-(1)^2$

Option C: $(50 n)2-(1)2$

Option D: $\left(50 n2\right)2-(1)^2$

Conclusion

Final Answer

Introduction

Q: What is the difference of squares formula?

Option A: $(10 n)^2-(1)2$

Option B: $\left(10 n^2\right)2-(1)^2$

Option C: $(50 n)^2-(1)2$

Option D: $\left(50 n^2\right)2-(1)^2$