Question

(a²-b²)(a+b) + (b²-c²)(b+c)+ (c²-a²)(c+a)

Answer 1

Answer:

(a²-b²)(a+b) + (b²-c²)(b+c)+ (c²-a²)(c+a)

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

= a ³ +  a² b - b²a - b³ + b³ + b²c - c²b - c³ + c³ + c²a - a²c - a³

=  a² b - b²a + b²c - c²b + c²a - a²c

= a² ( b - c ) + b² ( c - a ) + c² ( a - b ) ( answer )

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Answer 2

(a²-b²)(a+b) + (b²-c²)(b+c)+ (c²-a²)(c+a)

= a³ + a²b-ab²-b³ + b³+b²c-bc²-c³ + c³+ac²-a²c-a³

= a²b-ab²+b²c-bc²+ac²-a²c

= ab(a-b)+c²(a-b)+c(b²-a²)

= ab(a-b)+c²(a-b)-c((a+b)(a-b))

=(a-b)[ab+c²-c(a+b)]

=(a-b)[ab-cb+c²-ac]

=(a-b)[-b(c-a)+c(c-a)]

=(a-b)(c-b)(c-a)