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

asked by guest
on Nov 16, 2024 at 7:07 pm



You asked:

Evaluate the expression: \({b}^{2} \cdot {c}^{2} \cdot \left({b}^{2} - {c}^{2}\right) + {c}^{2} \cdot {a}^{2} \cdot \left({c}^{2} - {a}^{2}\right) + {a}^{2} \cdot {b}^{2} \cdot \left({a}^{2} - {b}^{2}\right)\)

MathBot Answer:

Evaluated



\(\displaystyle {b}^{2} \cdot {c}^{2} \cdot \left({b}^{2} - {c}^{2}\right) + {c}^{2} \cdot {a}^{2} \cdot \left({c}^{2} - {a}^{2}\right) + {a}^{2} \cdot {b}^{2} \cdot \left({a}^{2} - {b}^{2}\right) = a^{2} b^{2} \left(a^{2} - b^{2}\right) + a^{2} c^{2} \left(- a^{2} + c^{2}\right) + b^{2} c^{2} \left(b^{2} - c^{2}\right) \)

Expanded

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

Factored

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

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