Which Shows $53^2-47^2$ Being Evaluated Using The Difference Of Squares Method?A. $53^2-47^2=2809-2209=600$B. $53^2-47^2=(53+47)(53-47)=(100)(6)=600$C. $53^2-47^2=(53-47)^2=6^2=36$D.

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Introduction

The difference of squares method is a fundamental concept in algebra that allows us to simplify expressions of the form a2−b2a^2 - b^2. This method is based on the fact that a2−b2a^2 - b^2 can be factored as (a+b)(a−b)(a + b)(a - b). In this article, we will explore how to evaluate expressions using the difference of squares method and apply it to a specific problem.

Understanding the Difference of Squares Method

The difference of squares method is a factorization technique that allows us to rewrite an expression of the form a2−b2a^2 - b^2 as a product of two binomials: (a+b)(a + b) and (a−b)(a - b). This method is based on the following algebraic identity:

a2−b2=(a+b)(a−b)a^2 - b^2 = (a + b)(a - b)

To apply the difference of squares method, we need to identify the values of aa and bb in the given expression. Once we have identified the values of aa and bb, we can rewrite the expression as a product of two binomials using the formula above.

Evaluating Expressions Using the Difference of Squares Method

Let's consider an example to illustrate how to evaluate expressions using the difference of squares method. Suppose we want to evaluate the expression 532−47253^2 - 47^2. To apply the difference of squares method, we need to identify the values of aa and bb in the given expression.

In this case, we can see that a=53a = 53 and b=47b = 47. Now, we can rewrite the expression as a product of two binomials using the formula above:

532−472=(53+47)(53−47)53^2 - 47^2 = (53 + 47)(53 - 47)

Evaluating the Expression

Now that we have rewritten the expression as a product of two binomials, we can evaluate it by multiplying the two binomials:

(53+47)(53−47)=(100)(6)=600(53 + 47)(53 - 47) = (100)(6) = 600

Therefore, the value of the expression 532−47253^2 - 47^2 is 600.

Comparing the Results

Let's compare the result we obtained using the difference of squares method with the results given in the options:

A. 532−472=2809−2209=60053^2-47^2=2809-2209=600 B. 532−472=(53+47)(53−47)=(100)(6)=60053^2-47^2=(53+47)(53-47)=(100)(6)=600 C. 532−472=(53−47)2=62=3653^2-47^2=(53-47)^2=6^2=36 D.

We can see that options A and B give the same result as the one we obtained using the difference of squares method. However, option C is incorrect because it does not apply the difference of squares method correctly.

Conclusion

In this article, we have explored how to evaluate expressions using the difference of squares method. We have applied this method to a specific problem and obtained the correct result. We have also compared the results with the options given and identified the correct answer.

The difference of squares method is a powerful tool for simplifying expressions of the form a2−b2a^2 - b^2. By applying this method, we can rewrite expressions in a more convenient form and evaluate them more easily.

Frequently Asked Questions

Q: What is the difference of squares method?

A: The difference of squares method is a factorization technique that allows us to rewrite an expression of the form a2−b2a^2 - b^2 as a product of two binomials: (a+b)(a + b) and (a−b)(a - b).

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

A: To apply the difference of squares method, you need to identify the values of aa and bb in the given expression. Once you have identified the values of aa and bb, you can rewrite the expression as a product of two binomials using the formula (a+b)(a−b)(a + b)(a - b).

Q: What is the correct answer to the problem 532−47253^2 - 47^2?

A: The correct answer to the problem 532−47253^2 - 47^2 is 600.

References

Discussion

The difference of squares method is a fundamental concept in algebra that allows us to simplify expressions of the form a2−b2a^2 - b^2. This method is based on the fact that a2−b2a^2 - b^2 can be factored as (a+b)(a−b)(a + b)(a - b). In this article, we have explored how to evaluate expressions using the difference of squares method and applied it to a specific problem.

If you have any questions or comments about this article, please feel free to ask. We would be happy to hear from you and provide further clarification or examples.

Related Articles

Tags

  • difference of squares method
  • algebra
  • factorization techniques
  • expression evaluation
  • mathematics

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Introduction

The difference of squares method is a fundamental concept in algebra that allows us to simplify expressions of the form a2−b2a^2 - b^2. In this article, we will answer some of the most frequently asked questions about the difference of squares method.

Q: What is the difference of squares method?

A: The difference of squares method is a factorization technique that allows us to rewrite an expression of the form a2−b2a^2 - b^2 as a product of two binomials: (a+b)(a + b) and (a−b)(a - b).

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

A: To apply the difference of squares method, you need to identify the values of aa and bb in the given expression. Once you have identified the values of aa and bb, you can rewrite the expression as a product of two binomials using the formula (a+b)(a−b)(a + b)(a - b).

Q: What is the correct answer to the problem 532−47253^2 - 47^2?

A: The correct answer to the problem 532−47253^2 - 47^2 is 600.

Q: Can I use the difference of squares method to simplify expressions of the form a2+b2a^2 + b^2?

A: No, the difference of squares method can only be used to simplify expressions of the form a2−b2a^2 - b^2. If you want to simplify expressions of the form a2+b2a^2 + b^2, you need to use a different factorization technique.

Q: How do I know if an expression can be simplified using the difference of squares method?

A: To determine if an expression can be simplified using the difference of squares method, you need to check if the expression is of the form a2−b2a^2 - b^2. If it is, then you can use the difference of squares method to simplify it.

Q: Can I use the difference of squares method to simplify expressions with negative numbers?

A: Yes, you can use the difference of squares method to simplify expressions with negative numbers. For example, if you have the expression (−3)2−(−4)2(-3)^2 - (-4)^2, you can simplify it using the difference of squares method.

Q: How do I simplify expressions with negative numbers using the difference of squares method?

A: To simplify expressions with negative numbers using the difference of squares method, you need to follow the same steps as before. However, you need to be careful when simplifying expressions with negative numbers, as the signs of the terms may change.

Q: Can I use the difference of squares method to simplify expressions with fractions?

A: Yes, you can use the difference of squares method to simplify expressions with fractions. For example, if you have the expression (12)2−(34)2(\frac{1}{2})^2 - (\frac{3}{4})^2, you can simplify it using the difference of squares method.

Q: How do I simplify expressions with fractions using the difference of squares method?

A: To simplify expressions with fractions using the difference of squares method, you need to follow the same steps as before. However, you need to be careful when simplifying expressions with fractions, as the signs of the terms may change.

Q: Can I use the difference of squares method to simplify expressions with decimals?

A: Yes, you can use the difference of squares method to simplify expressions with decimals. For example, if you have the expression (2.5)2−(3.2)2(2.5)^2 - (3.2)^2, you can simplify it using the difference of squares method.

Q: How do I simplify expressions with decimals using the difference of squares method?

A: To simplify expressions with decimals using the difference of squares method, you need to follow the same steps as before. However, you need to be careful when simplifying expressions with decimals, as the signs of the terms may change.

Conclusion

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

Frequently Asked Questions

Q: What is the difference of squares method?

A: The difference of squares method is a factorization technique that allows us to rewrite an expression of the form a2−b2a^2 - b^2 as a product of two binomials: (a+b)(a + b) and (a−b)(a - b).

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

A: To apply the difference of squares method, you need to identify the values of aa and bb in the given expression. Once you have identified the values of aa and bb, you can rewrite the expression as a product of two binomials using the formula (a+b)(a−b)(a + b)(a - b).

Q: What is the correct answer to the problem 532−47253^2 - 47^2?

A: The correct answer to the problem 532−47253^2 - 47^2 is 600.

References

Discussion

The difference of squares method is a fundamental concept in algebra that allows us to simplify expressions of the form a2−b2a^2 - b^2. In this article, we have answered some of the most frequently asked questions about the difference of squares method.

If you have any questions or comments about this article, please feel free to ask. We would be happy to hear from you and provide further clarification or examples.

Related Articles

Tags

  • difference of squares method
  • algebra
  • factorization techniques
  • expression evaluation
  • mathematics