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