(x-y)(x-y) Simplify

Jasonbradley

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Jun 17, 2024

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Simplifying (x-y)(x-y)

The expression (x-y)(x-y) can be simplified using the distributive property or by recognizing it as a special product. Let's explore both methods.

Using the Distributive Property

The distributive property states that a(b+c) = ab + ac. We can apply this to our expression by considering (x-y) as a single term:

1. Distribute the first (x-y): (x-y)(x-y) = (x-y) * x + (x-y) * (-y)

2. Distribute again: = xx - yx + x*(-y) - y*(-y)

3. Simplify: = x² - xy - xy + y²

4. Combine like terms: = x² - 2xy + y²

Recognizing the Special Product

The expression (x-y)(x-y) is a perfect square trinomial. This is because it's the square of a binomial:

(x - y)² = (x - y)(x - y)

The general formula for a perfect square trinomial is:

(a - b)² = a² - 2ab + b²

Applying this to our problem, we see that:

• a = x
• b = y

Therefore, we can directly simplify:

(x - y)² = x² - 2xy + y²

Conclusion

Both methods lead to the same simplified expression: x² - 2xy + y². Using the distributive property demonstrates the process in detail, while recognizing the special product provides a shortcut for solving this type of problem.