Find maximum area of rectangle

Calculus Level 3

A rectangle's bottom is at y=0y=0

while its top corners are on the curve y=x(x1)2y=x{ (x-1) }^{ 2 } between x=0x=0 and x=1x=1. The maximum area of this rectangle can be expressed as

aabcd \dfrac { a\sqrt { a } -b }{ c\sqrt { d } }

where a a and d d are prime numbers. What is the sum a+b+c+d?a+b+c+d?

(Don't count a a twice)


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