Question

(-10square root 14 - square root 21)squared

Answer 1

To simplify the expression \((-10\sqrt{14} - \sqrt{21})^2\), we can use the formula for squaring a binomial, which is

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

In this case, we can identify:
- \(a = -10\sqrt{14}\)
- \(b = -\sqrt{21}\)

Now, we can find \(a^2\), \(b^2\), and \(2ab\).

1. **Calculating \(a^2\):**
\[
a^2 = (-10\sqrt{14})^2 = 100 \times 14 = 1400.
\]

2. **Calculating \(b^2\):**
\[
b^2 = (-\sqrt{21})^2 = 21.
\]

3. **Calculating \(2ab\):**
\[
2ab = 2 \cdot (-10\sqrt{14}) \cdot (-\sqrt{21}) = 20\sqrt{14 \cdot 21}.
\]

Now, we calculate \(14 \cdot 21\):
\[
14 \cdot 21 = 294.
\]

Thus,
\[
2ab = 20\sqrt{294}.
\]

Putting it all together:
\[
(-10\sqrt{14} - \sqrt{21})^2 = a^2 + 2ab + b^2 = 1400 + 20\sqrt{294} + 21.
\]

Now, combining the \(a^2\) and \(b^2\):
\[
1400 + 21 = 1421.
\]

So, the final simplified expression is:
\[
(-10\sqrt{14} - \sqrt{21})^2 = 1421 + 20\sqrt{294}.
\]