Find The Product Of { (b-11)^2$}$.A. { B^2+121$}$B. { B^2-121$}$C. { B^2+22b+121$}$D. { B^2-22b+121$}$

by ADMIN 103 views

Understanding the Problem

To find the product of {(b-11)^2$}$, we need to expand the given expression using the formula for squaring a binomial. The formula for squaring a binomial is (a−b)2=a2−2ab+b2{(a-b)^2 = a^2 - 2ab + b^2}. We can use this formula to expand the given expression.

Expanding the Expression

Using the formula for squaring a binomial, we can expand the given expression as follows:

(b−11)2=b2−2b(11)+112{(b-11)^2 = b^2 - 2b(11) + 11^2}

Simplifying the Expression

Now, we can simplify the expression by evaluating the terms:

(b−11)2=b2−22b+121{(b-11)^2 = b^2 - 22b + 121}

Comparing with the Options

Now, we can compare the simplified expression with the given options to find the correct product.

Option A: {b^2+121$}$

This option is incorrect because the simplified expression has a term −22b{-22b}, which is not present in this option.

Option B: {b^2-121$}$

This option is incorrect because the simplified expression has a term 121{121}, which is not present in this option.

Option C: {b^2+22b+121$}$

This option is incorrect because the simplified expression has a term −22b{-22b}, which is not present in this option.

Option D: {b^2-22b+121$}$

This option is correct because it matches the simplified expression.

Conclusion

The product of {(b-11)^2$}$ is {b^2-22b+121$}$. This can be verified by expanding the given expression using the formula for squaring a binomial and simplifying the resulting expression.

Final Answer

The final answer is {b^2-22b+121$}$.

Frequently Asked Questions

Q: What is the formula for squaring a binomial?

A: The formula for squaring a binomial is (a−b)2=a2−2ab+b2{(a-b)^2 = a^2 - 2ab + b^2}.

Q: How do I expand the given expression?

A: You can expand the given expression using the formula for squaring a binomial.

Q: How do I simplify the expression?

A: You can simplify the expression by evaluating the terms.

Q: How do I compare the simplified expression with the given options?

A: You can compare the simplified expression with the given options to find the correct product.

Related Topics

References

See Also

Frequently Asked Questions

Q: What is the formula for squaring a binomial?

A: The formula for squaring a binomial is (a−b)2=a2−2ab+b2{(a-b)^2 = a^2 - 2ab + b^2}.

Q: How do I expand the given expression?

A: You can expand the given expression using the formula for squaring a binomial. To do this, you need to substitute a=b{a = b} and b=11{b = 11} into the formula.

Q: How do I simplify the expression?

A: You can simplify the expression by evaluating the terms. In this case, the expression simplifies to b2−22b+121{b^2 - 22b + 121}.

Q: How do I compare the simplified expression with the given options?

A: You can compare the simplified expression with the given options to find the correct product. In this case, the correct product is b2−22b+121{b^2 - 22b + 121}.

Q: What is the final answer?

A: The final answer is b2−22b+121{b^2 - 22b + 121}.

Q: Can I use this formula to find the product of any binomial?

A: Yes, you can use this formula to find the product of any binomial. Just substitute the values of a{a} and b{b} into the formula and simplify the resulting expression.

Q: How do I know which option is correct?

A: You can compare the simplified expression with the given options to find the correct product. In this case, the correct product is b2−22b+121{b^2 - 22b + 121}.

Q: What if I get a different answer?

A: If you get a different answer, you may have made a mistake in expanding or simplifying the expression. Double-check your work and make sure you are using the correct formula.

Q: Can I use this formula to find the product of a binomial with a negative sign?

A: Yes, you can use this formula to find the product of a binomial with a negative sign. Just substitute the values of a{a} and b{b} into the formula and simplify the resulting expression.

Q: How do I know which option is correct when there are multiple options?

A: You can compare the simplified expression with the given options to find the correct product. In this case, the correct product is b2−22b+121{b^2 - 22b + 121}.

Related Topics

References

See Also

Additional Resources

Conclusion

The product of {(b-11)^2$}$ is {b^2 - 22b + 121$}$. This can be verified by expanding the given expression using the formula for squaring a binomial and simplifying the resulting expression.