Math Problem Statement

Multiply: (2x - 3y)^2

Solution

The expression in the image asks you to multiply (2x3y)2(2x - 3y)^2. This is a binomial square, and we can expand it using the formula:

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

In this case, a=2xa = 2x and b=3yb = 3y. Let's expand it:

(2x3y)2=(2x)22(2x)(3y)+(3y)2(2x - 3y)^2 = (2x)^2 - 2(2x)(3y) + (3y)^2

Now calculate each term:

  1. (2x)2=4x2(2x)^2 = 4x^2
  2. 2(2x)(3y)=12xy-2(2x)(3y) = -12xy
  3. (3y)2=9y2(3y)^2 = 9y^2

Putting it all together:

(2x3y)2=4x212xy+9y2(2x - 3y)^2 = 4x^2 - 12xy + 9y^2

The expanded form is 4x212xy+9y24x^2 - 12xy + 9y^2.

Would you like more details or have any further questions?

Here are 5 related questions for further practice:

  1. Expand (3x+4y)2(3x + 4y)^2.
  2. Multiply and simplify (5x2y)2(5x - 2y)^2.
  3. How would you expand (x5)2(x - 5)^2?
  4. Expand (2a+3b)2(2a + 3b)^2.
  5. What is the result of expanding (x6)2(x - 6)^2?

Tip: Always remember that the middle term in a binomial square is derived from multiplying the two terms twice.

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Math Problem Analysis

Mathematical Concepts

Algebra
Binomial Expansion
Quadratic Expressions

Formulas

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

Theorems

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Suitable Grade Level

Grades 9-10