Find the products of the following by using the appropriate identity:
`(x+5)(x-11)`

Answer

To find the product of the expression \((x + 5)(x - 11)\) using the appropriate identity, we can follow these steps:

### Step 1: Identify the Identity
We will use the identity for the product of two binomials:
\[ (a + b)(a - c) = a^2 + (b - c)a - bc \]
In our case, we can rewrite the expression as:
\[ (x + 5)(x - 11) \]
Here, \(a = x\), \(b = 5\), and \(c = 11\).

### Step 2: Apply the Identity
Using the identity, we can substitute \(a\), \(b\), and \(c\):
\[ (x + 5)(x - 11) = x^2 + (5 - 11)x - (5 \cdot 11) \]

### Step 3: Simplify the Expression
Now we will simplify each part:
1. Calculate \(5 - 11\):
\[ 5 - 11 = -6 \]
2. Calculate \(5 \cdot 11\):
\[ 5 \cdot 11 = 55 \]

Putting it all together, we have:
\[ (x + 5)(x - 11) = x^2 - 6x - 55 \]

### Final Answer
Thus, the product of \((x + 5)(x - 11)\) is:
\[ \boxed{x^2 - 6x - 55} \]

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