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The given expression is:

\[
18y - 6x - 3(x - 3y)(x - 3y)
\]

Let's break it down step by step:

### Step 1: Expand the product \((x - 3y)(x - 3y)\)
The expression \((x - 3y)(x - 3y)\) is a square binomial, so we can expand it as:

\[
(x - 3y)^2 = x^2 - 2(3y)(x) + (3y)^2 = x^2 - 6xy + 9y^2
\]

### Step 2: Substitute back into the original equation
Now substitute the expansion into the original expression:

\[
18y - 6x - 3(x^2 - 6xy + 9y^2)
\]

### Step 3: Distribute the \(-3\) across the expanded terms
Apply the distributive property:

\[
18y - 6x - 3x^2 + 18xy - 27y^2
\]

### Step 4: Combine like terms
In this case, there are no further like terms to combine, so the simplified expression is:

\[
-3x^2 + 18xy - 27y^2 - 6x + 18y
\]

Thus, the final simplified form is:

\[
-3x^2 + 18xy - 27y^2 - 6x + 18y
\]

Let me know if you'd like further clarification or details on any step.

Here are five related questions you can explore:
1. How do you expand binomials of higher degrees?
2. How does the distributive property work in polynomial expressions?
3. What are the rules for combining like terms in algebraic expressions?
4. How do you factor quadratic expressions like the expanded result?
5. Can this expression be factored further, or is it in its simplest form?

**Tip:** Always check for common factors after expanding an expression—sometimes you can simplify even further by factoring.

Solve the expression: 18y - 6x - 3(x - 3y)(x - 3y)

Learn how to simplify the algebraic expression 18y - 6x - 3(x - 3y)(x - 3y). This problem explores expanding binomials and using the distributive property to simplify algebraic expressions. Suitable for students in Grades 8-10.

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