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

Problem

x2*(b−c)+b2*(c+x)−c2*(x+b)

Solution

1. Expand the expression by distributing the terms outside the parentheses.

x2*b−x2*c+b2*c+b2*x−c2*x−c2*b

2. Rearrange the terms to group them by powers of x to treat the expression as a quadratic in x

(b−c)*x2+(b2−c2)*x+(b2*c−c2*b)

3. Factor the coefficients of each term.

(b−c)*x2+(b−c)*(b+c)*x+b*c*(b−c)

4. Factor out the common binomial factor (b−c) from the entire expression.

(b−c)*(x2+(b+c)*x+b*c)

5. Factor the quadratic trinomial x2+(b+c)*x+b*c by finding two numbers that multiply to b*c and add to b+c

(b−c)*(x+b)*(x+c)

Final Answer

x2*(b−c)+b2*(c+x)−c2*(x+b)=(b−c)*(x+b)*(x+c)

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