Find \(f(a+b)\)

Solution

Given: $$ f(x)=(x-a)^2(x-b)^2 $$

Put \(x=a+b\):

$$ f(a+b)=((a+b)-a)^2((a+b)-b)^2 $$

$$ =(b)^2(a)^2 $$

$$ =a^2b^2 $$

Hence, $$ \boxed{f(a+b)=a^2b^2} $$