To find the \( x^2 \) term in the expansion of \( (x - 5)^4 \) using the binomial theorem, we start with the binomial expansion formula:
\[ (a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k \]
In this case, we have \( a = x \), \( b = -5 \), and \( n = 4 \):
\[ (x - 5)^4 = \sum_{k=0}^{4} \binom{4}{k} x^{4-k} (-5)^k \]
To get the \( x^2 \) term, we need to find the term where \( 4 - k = 2 \), which means \( k = 2 \).
Now we will calculate that term:
\[ \text{For } k = 2: \]
\[ \binom{4}{2} x^{4-2} (-5)^2 \]
Calculating each component:
- \( \binom{4}{2} = \frac{4!}{2!(4-2)!} = \frac{4 \times 3}{2 \times 1} = 6 \)
- \( (-5)^2 = 25 \)
Now we substitute these values into the term:
\[ 6 \cdot x^{2} \cdot 25 = 150x^2 \]
Thus, the \( x^2 \) term in the expansion of \( (x - 5)^4 \) is:
\[ 150x^2 \]
The answer is \(\text{A. } 150x^2\).
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