Express in factored form: (a^2-b^2)^3 + (b^2-c^2)^3 + (c^2-a^2)^3/(a-b)^3 + (b-c)^3 + (c-a)^3

Question

Accepted Answer

(a + b)(b + c)(c + a). Each triple sums to zero, so numerator = 3(a^2-b^2)(b^2-c^2)(c^2-a^2) and denominator = 3(a-b)(b-c)(c-a). Cancelling leaves (a+b)(b+c)(c+a).

Express in factored form: $\frac{( a ^{2} - b ^{2} ) ^{3} + ( b ^{2} - c ^{2} ) ^{3} + ( c ^{2} - a ^{2} ) ^{3}}{( a - b ) ^{3} + ( b - c ) ^{3} + ( c - a ) ^{3}}$

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More Algebra practice

Express in factored form: (a−b)3+(b−c)3+(c−a)3(a2−b2)3+(b2−c2)3+(c2−a2)3​

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More Algebra practice

Express in factored form: $\frac{( a ^{2} - b ^{2} ) ^{3} + ( b ^{2} - c ^{2} ) ^{3} + ( c ^{2} - a ^{2} ) ^{3}}{( a - b ) ^{3} + ( b - c ) ^{3} + ( c - a ) ^{3}}$