To solve this problem, we need to correctly apply the algebraic expansion of \((b - x)^2\) and then substitute it into the given equation \(c^2 = h^2 + (b - x)^2\).
### Step-by-Step Solution:
1. Start with the expression \((b - x)^2\):
[tex]\[(b - x)^2\][/tex]
2. Expand this expression using the formula \((a - b)^2 = a^2 - 2ab + b^2\) where \(a = b\) and \(b = x\):
[tex]\[
(b - x)^2 = b^2 - 2bx + x^2
\][/tex]
3. Substitute the expanded form of \((b - x)^2\) into the original equation \(c^2 = h^2 + (b - x)^2\):
[tex]\[
c^2 = h^2 + (b^2 - 2bx + x^2)
\][/tex]
4. Combine like terms:
[tex]\[
c^2 = h^2 + b^2 - 2bx + x^2
\][/tex]
This is the expanded form of \((b - x)^2\) in the given equation.
### Conclusion:
The correct equation resulting from expanding \((b - x)^2\) and substituting it back into \(c^2 = h^2 + (b - x)^2\) is:
[tex]\[
c^2 = h^2 + b^2 - 2bx + x^2
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{c^2 = h^2 + b^2 - 2 b x + x^2}
\][/tex]
