prove that (a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3=3(a+b)(b+c)(c+a)(a-b)(b-c)(c-a)no

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rcmath | High School Teacher | (Level 1) Associate Educator

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Easier than proving one of them equal to the other directly, I will multiply and simplify both independtly and prove that they are equal to the same value.

Remember that








After using the difference of square formula, The right hand side of your equation will equal





If you rearange the terms in the last factor you will see that they are identical to the result we got form multiplying the left hand side, hence they are equal.





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