Express the following in the form a+bi
`(8+7i) (8-7i)`

Answer

To express the product \((8 + 7i)(8 - 7i)\) in the form \(a + bi\), we can follow these steps:

### Step 1: Identify the expression
We start with the expression:
\[ (8 + 7i)(8 - 7i) \]

### Step 2: Recognize the formula
This expression can be recognized as a difference of squares, which follows the formula:
\[ (x + y)(x - y) = x^2 - y^2 \]
Here, we can let \(x = 8\) and \(y = 7i\).

### Step 3: Apply the formula
Using the formula, we can rewrite the expression:
\[ (8 + 7i)(8 - 7i) = 8^2 - (7i)^2 \]

### Step 4: Calculate \(8^2\)
Now we calculate \(8^2\):
\[ 8^2 = 64 \]

### Step 5: Calculate \((7i)^2\)
Next, we calculate \((7i)^2\):
\[ (7i)^2 = 7^2 \cdot i^2 = 49 \cdot i^2 \]
Since \(i^2 = -1\), we have:
\[ (7i)^2 = 49 \cdot (-1) = -49 \]

### Step 6: Substitute back into the expression
Now we substitute back into the expression:
\[ 8^2 - (7i)^2 = 64 - (-49) = 64 + 49 \]

### Step 7: Simplify the expression
Now we simplify:
\[ 64 + 49 = 113 \]

### Step 8: Write in the form \(a + bi\)
Since there is no imaginary part, we can express this as:
\[ 113 + 0i \]

### Conclusion
Thus, the expression \((8 + 7i)(8 - 7i)\) in the form \(a + bi\) is:
\[ \boxed{113 + 0i} \]