You can put this solution on YOUR website! x^2+5xy+4y^2
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Rewrite as:
x^2+4xy+xy+4y^2
Factor the 1st two terms and the last two terms separately to get:
=x(x+4y)+y(x+4y)
Factor out the common factor to get:
=(x+4y)(x+y)
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I don't know if this is the "diamond" method; I have heard it
described as the AC Method.
Hope it helps.
Cheers,
Stan H.