Let's simplify the expression \((4x - 6)^2 - 6(4x - 6) + 6\).

### Step 1: Expand the square
Expand the first term \((4x - 6)^2\):
\[
(4x - 6)^2 = (4x - 6)(4x - 6) = 16x^2 - 48x + 36
\]

### Step 2: Distribute in the second term
Distribute \(-6\) in the second term:
\[
-6(4x - 6) = -24x + 36
\]

### Step 3: Combine all the terms
Now, substitute the expanded terms back into the original expression:
\[
16x^2 - 48x + 36 - 24x + 36 + 6
\]

### Step 4: Combine like terms
Combine the like terms:
\[
16x^2 - 72x + 78
\]

So, the simplified expression is:
\[
16x^2 - 72x + 78
\]

Would you like further clarification on any of these steps?

Here are 5 related questions to explore:
1. How do you expand binomials raised to higher powers?
2. What is the process for combining like terms in a polynomial?
3. How can you factor the quadratic expression \(16x^2 - 72x + 78\)?
4. What is the discriminant of the quadratic equation \(16x^2 - 72x + 78 = 0\)?
5. How would the expression change if the coefficients in the original expression were different?

**Tip:** When simplifying expressions, always follow the order of operations (parentheses, exponents, multiplication and division, addition and subtraction).

Learn how to simplify the expression (4x - 6)^2 - 6(4x - 6) + 6 with a detailed step-by-step solution. This problem involves expanding binomials, distributing terms, and combining like terms in a polynomial expression. Suitable for students in Grades 9-12 studying algebra and polynomials.

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