Math Problem Statement

(xy-6y)2

Solution

It looks like you're trying to simplify or expand the expression (xy6y)2(xy - 6y)^2. Let’s expand it using the binomial expansion formula:

(ab)2=a22ab+b2(a - b)^2 = a^2 - 2ab + b^2

Here, a=xya = xy and b=6yb = 6y. So, applying the formula:

(xy6y)2=(xy)22(xy)(6y)+(6y)2(xy - 6y)^2 = (xy)^2 - 2(xy)(6y) + (6y)^2

Now, let's simplify each term:

  1. (xy)2=x2y2(xy)^2 = x^2y^2
  2. 2(xy)(6y)=12xy2-2(xy)(6y) = -12xy^2
  3. (6y)2=36y2(6y)^2 = 36y^2

Thus, the expanded form is:

(xy6y)2=x2y212xy2+36y2(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(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 (xy6y)3(xy - 6y)^3?
  4. What happens if x=2x = 2 and y=3y = 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!

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Math Problem Analysis

Mathematical Concepts

Algebra
Binomial Expansion
Polynomials

Formulas

(a - b)^2 = a^2 - 2ab + b^2

Theorems

Binomial Expansion Theorem

Suitable Grade Level

Grades 9-10