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

Question

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

Answer 1

Expand some brackets:

x²(b-c)+b²c+b²x-c²x-bc².

Regroup: x²(b-c)+x(b²-c²)+bc(b-c)=x²(b-c)+x(b-c)(b+c)+bc(b-c).

Common factor is b-c:

(b-c)(x²+(b+c)x+bc)=(b-c)(x+b)(x+c)