It looks like you're trying to simplify or expand the expression \((xy - 6y)^2\). Let’s expand it using the binomial expansion formula:

\[
(a - b)^2 = a^2 - 2ab + b^2
\]

Here, \(a = xy\) and \(b = 6y\). So, applying the formula:

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

Now, let's simplify each term:

1. \((xy)^2 = x^2y^2\)
2. \(-2(xy)(6y) = -12xy^2\)
3. \((6y)^2 = 36y^2\)

Thus, the expanded form is:

\[
(xy - 6y)^2 = x^2y^2 - 12xy^2 + 36y^2
\]

Would you like more details on the steps or have any questions?

Here are 5 related questions:
1. How would you simplify \((x + y)^2\)?
2. What happens if you factor the expanded expression back?
3. Can this type of expansion be done for higher powers, such as \((xy - 6y)^3\)?
4. What happens if \(x = 2\) and \(y = 3\) in this expression?
5. How would the expansion change if the middle term was positive?

**Tip:** Always double-check your terms when expanding to avoid sign errors!

Learn how to expand the binomial expression (xy - 6y)^2 using the binomial expansion formula. This detailed step-by-step guide covers key algebraic concepts such as polynomials and binomial expansion, suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation