Question

(5 - 4square root 11)squared

Answer 1

To simplify the expression \((5 - 4\sqrt{11})^2\), we can apply the formula for the square of a binomial, which is given by:

\[
(a - b)^2 = a^2 - 2ab + b^2
\]

In this case, let \(a = 5\) and \(b = 4\sqrt{11}\). Now we can calculate each part:

1. **Calculate \(a^2\)**:
\[
a^2 = 5^2 = 25
\]

2. **Calculate \(b^2\)**:
\[
b^2 = (4\sqrt{11})^2 = 16 \cdot 11 = 176
\]

3. **Calculate \(2ab\)**:
\[
2ab = 2 \cdot 5 \cdot 4\sqrt{11} = 40\sqrt{11}
\]

Now, substituting these values back into the binomial expansion formula:

\[
(5 - 4\sqrt{11})^2 = 25 - 40\sqrt{11} + 176
\]

Combining like terms:

\[
25 + 176 = 201
\]

So, we have:

\[
(5 - 4\sqrt{11})^2 = 201 - 40\sqrt{11}
\]

Therefore, the final answer is:

\[
\boxed{201 - 40\sqrt{11}}
\]