Question
(8 - 8square root 3)squared
Answers
GPT-4o mini
To simplify \((8 - 8\sqrt{3})^2\), we can use the binomial expansion formula:
\[
(a - b)^2 = a^2 - 2ab + b^2
\]
In this case, let \(a = 8\) and \(b = 8\sqrt{3}\). Now we can compute each term:
1. \(a^2 = 8^2 = 64\)
2. \(b^2 = (8\sqrt{3})^2 = 64 \cdot 3 = 192\)
3. \(2ab = 2 \cdot 8 \cdot 8\sqrt{3} = 128\sqrt{3}\)
Putting it all together:
\[
(8 - 8\sqrt{3})^2 = a^2 - 2ab + b^2 = 64 - 128\sqrt{3} + 192
\]
Now, combine like terms:
\[
64 + 192 = 256
\]
So the final result is:
\[
(8 - 8\sqrt{3})^2 = 256 - 128\sqrt{3}
\]
\[
(a - b)^2 = a^2 - 2ab + b^2
\]
In this case, let \(a = 8\) and \(b = 8\sqrt{3}\). Now we can compute each term:
1. \(a^2 = 8^2 = 64\)
2. \(b^2 = (8\sqrt{3})^2 = 64 \cdot 3 = 192\)
3. \(2ab = 2 \cdot 8 \cdot 8\sqrt{3} = 128\sqrt{3}\)
Putting it all together:
\[
(8 - 8\sqrt{3})^2 = a^2 - 2ab + b^2 = 64 - 128\sqrt{3} + 192
\]
Now, combine like terms:
\[
64 + 192 = 256
\]
So the final result is:
\[
(8 - 8\sqrt{3})^2 = 256 - 128\sqrt{3}
\]