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i want sage to do that for me!
Okay then let Sage do it for you:
sage: var('a, b, c, d, e')
(a, b, c, d, e)
sage: P = a*d + b*c + d^2 + d*e
sage: P.subs(e=(a + b - d)).expand()
b*c + 2*a*d + b*d
This is exactly what you want: It simplified the expression given that a + b = d + e.
