Simplify (4m+ 5n)² + ( 5m + 4n)² +2mn
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4m+5n)2+(5m+4n)2
Using (a+b)2=a2+2ab+b2 we get,
=[(4m)2+2(4m)(5n)+(5n)2]+[(5m)2+2(5m)(4n)+(4n)2]
=16m2+40mn+25n2+25m2+40mn+16n2
=41m2+80mn+41n2
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