(a-b)(a-b)(b-c)(a+b)(a+c)(b+c)+(a+b)(b+c)(a+c)(aac+bba+ccb)+abc(a-b)(a-c)(b-c)
You asked:
MathBot Answer:
Evaluated
\(\displaystyle \left(a - b\right) \cdot \left(a - b\right) \cdot \left(b - c\right) \cdot \left(a + b\right) \cdot \left(a + c\right) \cdot \left(b + c\right) + \left(a + b\right) \cdot \left(b + c\right) \cdot \left(a + c\right) \cdot \left(a a c + b b a + c c b\right) + a b \cdot c \cdot \left(a - b\right) \cdot \left(a - c\right) \cdot \left(b - c\right) = a b c \left(a - b\right) \left(a - c\right) \left(b - c\right) + \left(a - b\right)^{2} \left(a + b\right) \left(a + c\right) \left(b - c\right) \left(b + c\right) + \left(a + b\right) \left(a + c\right) \left(b + c\right) \left(a^{2} c + b^{2} a + c^{2} b\right) \)
Expanded
\[\left(a - b\right) \cdot \left(a - b\right) \cdot \left(b - c\right) \cdot \left(a + b\right) \cdot \left(a + c\right) \cdot \left(b + c\right) + \left(a + b\right) \cdot \left(b + c\right) \cdot \left(a + c\right) \cdot \left(a a c + b b a + c c b\right) + a b \cdot c \cdot \left(a - b\right) \cdot \left(a - c\right) \cdot \left(b - c\right) = a^{4} b^{2} + a^{4} b c + 4 a^{3} b^{2} c + 2 a^{3} c^{2} b + 4 a^{2} b^{2} c^{2} + 4 a^{2} c^{3} b + b^{5} a + 2 b^{3} c^{2} a + 2 b^{2} c^{3} a + c^{4} a b + b^{5} c + b^{2} c^{4}\]
Factored
\[\left(a - b\right) \cdot \left(a - b\right) \cdot \left(b - c\right) \cdot \left(a + b\right) \cdot \left(a + c\right) \cdot \left(b + c\right) + \left(a + b\right) \cdot \left(b + c\right) \cdot \left(a + c\right) \cdot \left(a a c + b b a + c c b\right) + a b \cdot c \cdot \left(a - b\right) \cdot \left(a - c\right) \cdot \left(b - c\right) = b \left(a^{4} b + a^{4} c + 4 a^{3} b c + 2 a^{3} c^{2} + 4 a^{2} c^{2} b + 4 a^{2} c^{3} + b^{4} a + 2 b^{2} c^{2} a + 2 c^{3} a b + c^{4} a + b^{4} c + c^{4} b\right)\]