https://file.aiquickdraw.com/mathbot/file/1725710324698x4mxrqqn.jpg

The expression shown in the image is \( (2x - y)(3x - y) \), and the instruction appears to ask for the expansion of this product.

Let's expand it step by step:

\[
(2x - y)(3x - y) = 2x(3x - y) - y(3x - y)
\]

First, distribute \( 2x \) to both terms inside the second parenthesis:

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

Next, distribute \( -y \) to both terms inside the second parenthesis:

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

Now, combine all the terms:

\[
6x^2 - 2xy - 3xy + y^2 = 6x^2 - 5xy + y^2
\]

Thus, the expanded form of the expression is:

\[
6x^2 - 5xy + y^2
\]

Would you like further clarification on this expansion, or do you have any additional questions?

Here are 5 related questions for practice:
1. How would you expand \( (x - y)(x + y) \)?
2. Can you factor \( 6x^2 - 5xy + y^2 \) back into two binomials?
3. What is the expansion of \( (2x + y)(3x + y) \)?
4. How does the distributive property work in expanding binomials?
5. What happens if you have three terms, e.g., \( (x + 1)(x - 2)(x + 3) \)?

**Tip:** When expanding binomials, always distribute each term in the first binomial to every term in the second binomial for accurate results.

Explore the algebraic expansion of the binomial expression (2x - y)(3x - y). Learn how to apply the distributive property and combine like terms to arrive at the final expanded form, 6x^2 - 5xy + y^2. This example is suitable for students in Grades 9-12 and covers core algebra concepts.

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