I’m not sure on how to get from this...

x^2(b-c)+b^2(c+x)-c^2(x+b)

to this...

(b-c)(x+b)(x+c)

without having to expand everything first and rather putting the equation into an ax^2+ bx + c format

x^2(b-c)+b^2(c+x)-c^2(x+b)

to this...

(b-c)(x+b)(x+c)

without having to expand everything first and rather putting the equation into an ax^2+ bx + c format