Answer
$(x-3)(b+c)(b-c)$
Work Step by Step
The product of a binomial sum and a binomial difference is: $(A+B)(A-B)=A^2-B^2$.
The square of a binomial sum is: $(A+B)^2=A^2+2AB+B^2$.
The square of a binomial difference is: $(A-B)^2=A^2-2AB+B^2$.
Hence:
$b^2(x-3)+c^2(3-x)=\\=b^2(x-3)-c^2(x-3)\\=(x-3)(b^2-c^2)\\=(x-3)(b+c)(b-c)$
