Evaluate The Expression A 2 − 2 A B − B 2 A^2 - 2ab - B^2 A 2 − 2 Ab − B 2 Given A = 3 A = 3 A = 3 And B = − 4 B = -4 B = − 4 .

Mar 7, 2025 by ADMIN 128 views

Evaluate the Expression $a^2 - 2ab - b^2$ Given $a = 3$ and $b = -4$

Introduction

In algebra, evaluating expressions is a crucial skill that helps us solve problems and understand mathematical concepts. In this article, we will evaluate the expression $a^2 - 2ab - b^2$ given the values of $a$ and $b$ . We will use the given values of $a = 3$ and $b = -4$ to substitute into the expression and simplify it.

Understanding the Expression

The given expression is a quadratic expression in the form of $a^2 - 2ab - b^2$ . This expression can be factored as $(a - b)^2$ . We will use this factored form to simplify the expression.

Substituting the Values of $a$ and $b$

We are given the values of $a = 3$ and $b = -4$ . We will substitute these values into the expression $a^2 - 2ab - b^2$ .

Evaluating the Expression

To evaluate the expression, we will substitute the values of $a$ and $b$ into the expression.

import sympy
a = 3
b = -4

expression = a2 - 2ab - b2

result = sympy.simplify(expression)
print(result)

Simplifying the Expression

The expression $a^2 - 2ab - b^2$ can be simplified using the factored form $(a - b)^2$ . We will use this factored form to simplify the expression.

import sympy

a = 3
b = -4

expression = (a - b)**2

result = sympy.simplify(expression)
print(result)

Conclusion

In this article, we evaluated the expression $a^2 - 2ab - b^2$ given the values of $a = 3$ and $b = -4$ . We used the factored form $(a - b)^2$ to simplify the expression. The final result is $25$ .

Final Answer

The final answer is $\boxed{25}$ .

References

[1] Khan Academy. (n.d.). Factoring Quadratic Expressions. Retrieved from https://www.khanacademy.org/math/algebra/x2factors/x2factors
[2] Mathway. (n.d.). Algebra Calculator. Retrieved from https://www.mathway.com/

Additional Resources

[1] Algebra.com. (n.d.). Algebra Calculator. Retrieved from https://www.algebra.com/
[2] Wolfram Alpha. (n.d.). Algebra Calculator. Retrieved from https://www.wolframalpha.com/

Introduction

In our previous article, we evaluated the expression $a^2 - 2ab - b^2$ given the values of $a = 3$ and $b = -4$ . We used the factored form $(a - b)^2$ to simplify the expression. In this article, we will answer some frequently asked questions related to evaluating the expression $a^2 - 2ab - b^2$ .

Q&A

Q: What is the factored form of the expression $a^2 - 2ab - b^2$ ?

A: The factored form of the expression $a^2 - 2ab - b^2$ is $(a - b)^2$ .

Q: How do I evaluate the expression $a^2 - 2ab - b^2$ given the values of $a$ and $b$ ?

A: To evaluate the expression $a^2 - 2ab - b^2$ given the values of $a$ and $b$ , you can substitute the values of $a$ and $b$ into the expression and simplify it.

Q: What is the final result of evaluating the expression $a^2 - 2ab - b^2$ given the values of $a = 3$ and $b = -4$ ?

A: The final result of evaluating the expression $a^2 - 2ab - b^2$ given the values of $a = 3$ and $b = -4$ is $25$ .

Q: Can I use a calculator to evaluate the expression $a^2 - 2ab - b^2$ ?

A: Yes, you can use a calculator to evaluate the expression $a^2 - 2ab - b^2$ . However, it's always a good idea to understand the underlying math and be able to simplify the expression manually.

Q: How do I simplify the expression $a^2 - 2ab - b^2$ ?

A: To simplify the expression $a^2 - 2ab - b^2$ , you can use the factored form $(a - b)^2$ and then simplify the expression further if possible.

Q: What are some common mistakes to avoid when evaluating the expression $a^2 - 2ab - b^2$ ?

A: Some common mistakes to avoid when evaluating the expression $a^2 - 2ab - b^2$ include:

Not substituting the values of $a$ and $b$ into the expression
Not simplifying the expression using the factored form
Not checking for any common factors or simplifications

Conclusion

In this article, we answered some frequently asked questions related to evaluating the expression $a^2 - 2ab - b^2$ . We hope that this article has been helpful in clarifying any doubts you may have had about evaluating this expression.

Final Answer

The final answer is $\boxed{25}$ .

References

[1] Khan Academy. (n.d.). Factoring Quadratic Expressions. Retrieved from https://www.khanacademy.org/math/algebra/x2factors/x2factors
[2] Mathway. (n.d.). Algebra Calculator. Retrieved from https://www.mathway.com/

Additional Resources

[1] Algebra.com. (n.d.). Algebra Calculator. Retrieved from https://www.algebra.com/
[2] Wolfram Alpha. (n.d.). Algebra Calculator. Retrieved from https://www.wolframalpha.com/

Evaluate The Expression A 2 − 2 A B − B 2 A^2 - 2ab - B^2 A 2 − 2 Ab − B 2 Given A = 3 A = 3 A = 3 And B = − 4 B = -4 B = − 4 .

Introduction

Understanding the Expression

Substituting the Values of $a$ and $b$

Evaluating the Expression

Simplifying the Expression

Conclusion

Final Answer

Related Topics

References

Additional Resources

Introduction

Q&A

Q: What is the factored form of the expression $a^2 - 2ab - b^2$ ?

Q: How do I evaluate the expression $a^2 - 2ab - b^2$ given the values of $a$ and $b$ ?

Q: What is the final result of evaluating the expression $a^2 - 2ab - b^2$ given the values of $a = 3$ and $b = -4$ ?

Q: Can I use a calculator to evaluate the expression $a^2 - 2ab - b^2$ ?

Q: How do I simplify the expression $a^2 - 2ab - b^2$ ?

Q: What are some common mistakes to avoid when evaluating the expression $a^2 - 2ab - b^2$ ?

Conclusion

Final Answer

Related Topics

References

Additional Resources

Introduction

Understanding the Expression

Substituting the Values of aaa and bbb

Evaluating the Expression

Simplifying the Expression

Conclusion

Final Answer

Related Topics

References

Additional Resources

Introduction

Q&A

Q: What is the factored form of the expression a2−2ab−b2a^2 - 2ab - b^2a2−2ab−b2?

Q: How do I evaluate the expression a2−2ab−b2a^2 - 2ab - b^2a2−2ab−b2 given the values of aaa and bbb?

Q: What is the final result of evaluating the expression a2−2ab−b2a^2 - 2ab - b^2a2−2ab−b2 given the values of a=3a = 3a=3 and b=−4b = -4b=−4?

Q: Can I use a calculator to evaluate the expression a2−2ab−b2a^2 - 2ab - b^2a2−2ab−b2?

Q: How do I simplify the expression a2−2ab−b2a^2 - 2ab - b^2a2−2ab−b2?

Q: What are some common mistakes to avoid when evaluating the expression a2−2ab−b2a^2 - 2ab - b^2a2−2ab−b2?

Conclusion

Final Answer

Related Topics

References

Additional Resources

Substituting the Values of $a$ and $b$

Q: What is the factored form of the expression $a^2 - 2ab - b^2$ ?

Q: How do I evaluate the expression $a^2 - 2ab - b^2$ given the values of $a$ and $b$ ?

Q: What is the final result of evaluating the expression $a^2 - 2ab - b^2$ given the values of $a = 3$ and $b = -4$ ?

Q: Can I use a calculator to evaluate the expression $a^2 - 2ab - b^2$ ?

Q: How do I simplify the expression $a^2 - 2ab - b^2$ ?

Q: What are some common mistakes to avoid when evaluating the expression $a^2 - 2ab - b^2$ ?