(3х - у) * (у + 3х)

To simplify the expression \((3x - y) * (y + 3x)\), we can use the distributive property (also known as the FOIL method for binomials).

Here's a step-by-step breakdown of the multiplication:

1. First terms: \(3x * y = 3xy\)
2. Outer terms: \(3x * 3x = 9x^2\)
3. Inner terms: \(-y * y = -y^2\)
4. Last terms: \(-y * 3x = -3xy\)

Now, combine all these results:

\[ 3xy + 9x^2 - y^2 - 3xy \]

Now, combine like terms:

• The \(3xy\) and \(-3xy\) cancel out.

So we are left with:

\[ 9x^2 - y^2 \]

Thus, the simplified form of the expression \((3x - y) * (y + 3x)\) is:

\[ 9x^2 - y^2 \]