(a+b+c)*(b+c-a)*(a-b+c)*(a+b-c)

asked by guest
on Dec 26, 2024 at 9:10 am



You asked:

Evaluate the expression: \(\left(a + b + c\right) \left(b + c - a\right) \left(a - b + c\right) \left(a + b - c\right)\)

MathBot Answer:

Evaluated



\(\displaystyle \left(a + b + c\right) \left(b + c - a\right) \left(a - b + c\right) \left(a + b - c\right) = \left(- a + b + c\right) \left(a - b + c\right) \left(a + b - c\right) \left(a + b + c\right) \)

Expanded

\[\left(a + b + c\right) \left(b + c - a\right) \left(a - b + c\right) \left(a + b - c\right) = - a^{4} + 2 a^{2} b^{2} + 2 a^{2} c^{2} - b^{4} + 2 b^{2} c^{2} - c^{4}\]

Factored

\[\left(a + b + c\right) \left(b + c - a\right) \left(a - b + c\right) \left(a + b - c\right) = - \left(a - b - c\right) \left(a - b + c\right) \left(a + b - c\right) \left(a + b + c\right)\]

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