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

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SUMMARY

The equation x² · y² is not equal to (x - y)(x + y). The correct identity is x² - y² = (x - y)(x + y). Additionally, the expression xy - y² can be factored as (√(xy) - y)(√(xy) + y). For example, substituting x = 8 and y = 2 demonstrates these identities clearly.

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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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