Math Problem Statement

(4x - y)^2

Solution

The problem shown in the image is:

(4xy)2(4x - y)^2

This is a binomial square, and it can be expanded using the formula for the square of a binomial:

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

Here, a=4xa = 4x and b=yb = y. Applying the formula:

(4xy)2=(4x)22(4x)(y)+y2(4x - y)^2 = (4x)^2 - 2(4x)(y) + y^2

Now, simplify each term:

  1. (4x)2=16x2(4x)^2 = 16x^2
  2. 2(4x)(y)=8xy-2(4x)(y) = -8xy
  3. y2=y2y^2 = y^2

So, the expanded form is:

16x28xy+y216x^2 - 8xy + y^2

Would you like more details on how this was derived, or do you have any further questions?

Here are five related questions for practice:

  1. Expand and simplify (5a2b)2(5a - 2b)^2.
  2. Expand and simplify (3x+2)2(3x + 2)^2.
  3. What is the result of (6x3)2(6x - 3)^2?
  4. Expand (2xy)2(2x - y)^2 and explain each step.
  5. What happens when you square a sum, such as (x+3)2(x + 3)^2?

Tip: When squaring binomials, always use the binomial square formula to quickly expand and simplify.

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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