3|x+y|to the power of 2-(xy)to the power of 2

The expression you've given is:

\[
(3|x + y|)^2 - (xy)^2
\]

To simplify or expand this expression, let's break it down step by step:

### Step 1: Expand the first term
The first term is \((3|x + y|)^2\). This can be expanded as:

\[
(3|x + y|)^2 = 9(x + y)^2
\]

### Step 2: Expand the second term
The second term is \((xy)^2\), which is already in its simplest form.

### Step 3: Substitute and combine
Now, substitute the expanded forms back into the original expression:

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

This is the simplified form of the given expression. If needed, you can expand \((x + y)^2\) further:

\[
(x + y)^2 = x^2 + 2xy + y^2
\]

So the expression becomes:

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

Or:

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

This is the fully expanded and simplified form of the expression.

Would you like more details or explanations on any of these steps?

### Relative Questions:

1. How do you expand binomials like \((x + y)^2\)?
2. What are some common identities used in algebraic expansion?
3. How do you factor a quadratic expression like \(9(x^2 + 2xy + y^2)\)?
4. How do you solve equations involving absolute values?
5. What are the properties of exponents used in algebra?

### Tip:
When expanding expressions, always look for opportunities to factor or simplify terms to make the expression easier to work with later on.

Learn how to simplify the expression 3|x + y|^2 - (xy)^2 with detailed step-by-step instructions. This problem involves algebraic concepts such as absolute value, exponents, and the expansion of binomials. Suitable for high school students.

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