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(2x + 3y)^2 – (2x – 3y)^2 = 360 show that xy is a multiple of 5

Expand first brackets:

4x2+6xy+6xy+9y2

Expand second brackets:

4xy2-6xy-6xy+9y2

Subtract the second expansion from the first one, being careful of the double negative:

=24xy

Then, back into the original equation:

24xy=360

Divide both sides by 24:

xy=15

Divide by 5:

(xy)/5=3

The result is an integer, so xy is a multiple of 5

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