High School Why is x2 . y2 not equal to (x-y) (x+y)?

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The expression x²·y² is not equal to (x-y)(x+y); rather, x²-y² equals (x-y)(x+y). The discussion clarifies that while x²-y² can be factored using the difference of squares, xy-y² does not follow the same factorization rule. Substituting specific values, such as x=8 and y=2, can help illustrate these relationships. The distinction between these algebraic identities is crucial for understanding polynomial factorization. Understanding these differences aids in grasping fundamental algebraic concepts.
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why x2 . y2 = (x-y) (x+y) and xy . y2 cannot be (x-y) (y+y)
 
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Atqiya said:
why x2 . y2 = (x-y) (x+y) and xy . y2 cannot be (x-y) (y+y)
If by x2 . y2 you mean ##x^2\cdot y^2##, then it is not equal to ##(x-y)(x+y)##.
It is true that ##x^2-y^2=(x-y)(x+y)##. It is also true that ##xy-y^2=(\sqrt{xy}-y)(\sqrt{xy}+y)## . Try substituting ##x=8## and ##y=2## to see how it works.
 
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Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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