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).