Write down the first three terms is the following expansions
`(1 + 4x)^(-4)`

Answer

To find the first three terms of the expansion of \((1 + 4x)^{-4}\), we can use the Binomial Theorem, which states that:

\[ (1 + x)^{-n} = \sum_{k=0}^{\infty} \binom{-n}{k} x^k \]

where \(\binom{-n}{k} = \frac{(-n)(-n-1)(-n-2)\cdots(-n-k+1)}{k!}\).

In our case, we have \(n = 4\) and \(x = 4x\).

### Step 1: Identify the terms
We need to find the first three terms of the expansion:
1. The first term (\(k=0\)):
\[ T_0 = \binom{-4}{0} (4x)^0 = 1 \]

2. The second term (\(k=1\)):
\[ T_1 = \binom{-4}{1} (4x)^1 = -4(4x) = -16x \]

3. The third term (\(k=2\)):
\[ T_2 = \binom{-4}{2} (4x)^2 = \frac{(-4)(-5)}{2!} (16x^2) = \frac{20}{2} (16x^2) = 10 \cdot 16x^2 = 160x^2 \]

### Step 2: Combine the terms
Now, we combine the first three terms:
\[ 1 - 16x + 160x^2 \]

### Final Result
Thus, the first three terms of the expansion of \((1 + 4x)^{-4}\) are:
\[ 1 - 16x + 160x^2 \]