Find the products of the following by using the appropriate identity:
`(x-9)(x-7)`

Answer

To find the product of the expression \((x-9)(x-7)\) 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:
\[ (x + a)(x + b) = x^2 + (a + b)x + ab \]
In our case, we can rewrite the expression as:
\[ (x - 9)(x - 7) = (x + (-9))(x + (-7)) \]
Here, \(a = -9\) and \(b = -7\).

### Step 2: Calculate \(a + b\)
Now, we need to calculate \(a + b\):
\[ a + b = -9 + (-7) = -16 \]

### Step 3: Calculate \(ab\)
Next, we calculate \(ab\):
\[ ab = (-9)(-7) = 63 \]

### Step 4: Substitute into the identity
Now we can substitute \(a + b\) and \(ab\) into the identity:
\[ (x - 9)(x - 7) = x^2 + (-16)x + 63 \]

### Step 5: Write the final expression
Thus, the final expression is:
\[ x^2 - 16x + 63 \]

### Final Answer
The product of \((x-9)(x-7)\) is:
\[ x^2 - 16x + 63 \]

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