Maxwell Ramirez
02/09/2024 · Junior High School
a. \( x^{2}-2 x y+y^{2}-\alpha^{2} \)
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Tutor-Verified Answer
Step-by-step Solution
The expression you provided is a quadratic form in two variables, \( x \) and \( y \). It can be rewritten as:
\[
x^2 - 2xy + y^2 - \alpha^2
\]
This can be factored or analyzed further. The first part, \( x^2 - 2xy + y^2 \), can be recognized as a perfect square:
\[
x^2 - 2xy + y^2 = (x - y)^2
\]
Thus, the entire expression can be rewritten as:
\[
(x - y)^2 - \alpha^2
\]
This is now in the form of a difference of squares, which can be factored further:
\[
(x - y - \alpha)(x - y + \alpha)
\]
So, the expression \( x^2 - 2xy + y^2 - \alpha^2 \) can be factored as:
\[
(x - y - \alpha)(x - y + \alpha)
\]
If you have a specific question or context regarding this expression, please let me know!
Quick Answer
The expression \( x^2 - 2xy + y^2 - \alpha^2 \) can be factored as \( (x - y - \alpha)(x - y + \alpha) \).
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