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The expression provided is \((\sqrt{a} - \sqrt{ac})\), and we are asked to find the product of this expression with its conjugate.

### Step 1: Identify the conjugate.
The conjugate of \((\sqrt{a} - \sqrt{ac})\) is \((\sqrt{a} + \sqrt{ac})\). 

### Step 2: Multiply the expression by its conjugate.
The product of \((\sqrt{a} - \sqrt{ac})\) and \((\sqrt{a} + \sqrt{ac})\) follows the difference of squares formula:

\[
(\sqrt{a} - \sqrt{ac})(\sqrt{a} + \sqrt{ac}) = (\sqrt{a})^2 - (\sqrt{ac})^2
\]

### Step 3: Simplify each term.
- \((\sqrt{a})^2 = a\)
- \((\sqrt{ac})^2 = ac\)

### Step 4: Calculate the final expression.
Now, subtract the terms:

\[
a - ac = a(1 - c)
\]

Thus, the product of \((\sqrt{a} - \sqrt{ac})\) and its conjugate is \(a(1 - c)\).

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the general form of the difference of squares?
2. How do you find the conjugate of a binomial with square roots?
3. Can the process for finding the conjugate be applied to complex numbers?
4. How does multiplying conjugates simplify expressions with square roots?
5. Why is the product of a binomial and its conjugate always real?

**Tip:** When multiplying conjugates, using the difference of squares formula can greatly simplify calculations!

Which of the following is the product of (√a - √ac) and its conjugate?

Find the product of (√a - √ac) and its conjugate using the difference of squares formula. Learn how to simplify expressions involving radicals and apply the conjugate in algebraic problems. Suitable for students in Grades 9-11.

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