Question
Find the numerical equivalent of 81⋅83
.(1 point)
Responses
4,096
4,096
512
512
520
520
84
.(1 point)
Responses
4,096
4,096
512
512
520
520
84
Answers
Answered by
GPT-4o mini
To find the numerical equivalent of \(81 \times 83\), we can use the difference of squares formula.
We know that:
\[
(a+b)(a-b) = a^2 - b^2
\]
In this case, we can express \(81\) and \(83\) as:
\[
81 = 82 - 1 \quad \text{and} \quad 83 = 82 + 1
\]
So we can rewrite the expression as:
\[
81 \times 83 = (82 - 1)(82 + 1) = 82^2 - 1^2
\]
Calculating \(82^2\):
\[
82^2 = 6724
\]
Thus:
\[
81 \times 83 = 6724 - 1 = 6723
\]
Now we need to find if any of the provided responses match this calculation. It appears none of the provided numerical options (4,096, 512, 520, 84) fits the result of \(81 \times 83 = 6723\).
However, if you directly calculate \(81 \cdot 83\):
\[
81 \cdot 83 = 81 \cdot (80 + 3) = 81 \cdot 80 + 81 \cdot 3 = 6480 + 243 = 6723
\]
The provided answers do not match. The correct answer to \(81 \cdot 83\) is indeed \(6723\). Please check the response options again for possible inclusion or adjustments.
We know that:
\[
(a+b)(a-b) = a^2 - b^2
\]
In this case, we can express \(81\) and \(83\) as:
\[
81 = 82 - 1 \quad \text{and} \quad 83 = 82 + 1
\]
So we can rewrite the expression as:
\[
81 \times 83 = (82 - 1)(82 + 1) = 82^2 - 1^2
\]
Calculating \(82^2\):
\[
82^2 = 6724
\]
Thus:
\[
81 \times 83 = 6724 - 1 = 6723
\]
Now we need to find if any of the provided responses match this calculation. It appears none of the provided numerical options (4,096, 512, 520, 84) fits the result of \(81 \times 83 = 6723\).
However, if you directly calculate \(81 \cdot 83\):
\[
81 \cdot 83 = 81 \cdot (80 + 3) = 81 \cdot 80 + 81 \cdot 3 = 6480 + 243 = 6723
\]
The provided answers do not match. The correct answer to \(81 \cdot 83\) is indeed \(6723\). Please check the response options again for possible inclusion or adjustments.