Factorize 1.bc(b-c)+ca(c-a)+ab(a-b)

2.a(b-c)^2+b(c-a)^2+c(a-b)^2+8abc

3.(b^3+c^3)(b-c)+(c^3+a^3)(c-a)+(a^3+b^3)(a-b)

1
2. (a+b)(b+c)(c+a)
3. (a+b+c)(a-b)(b-c)(c-a)
I can explain them to you but I need to know which class you are in.
And a little tip DON'T EXPAND THE GIVEN EXPRESSION SO AS TO FACTORISE
thanx juttuc - what is ur name?

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2014-11-09T14:06:10+05:30

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b^2c - bc^2+c^2a-ca^2+ab(a-b)=c(b^2-a^2)+c^2(a-b)+ab(a-b)\\\\=(a-b)[-c(b+a)+c^2+ab)]\\\\=(a-b)(c^2+ab-bc-ca)\\\\(a-b)(b(a-c)+c(c-a))\\\\(a-b)(c-b)(c-a)

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a(b-c)^2+b(c-a)^2+c(a-b)^2+8abc\\\\=ab^2+ac^2-2abc+bc^2+ba^2-2abc+c(a-b)^2+8abc\\\\=ab(a+b)+c^2(a+b)+4abc+c(a-b)^2\\\\=(a+b)(ab+c^2)+4abc+ca^2+cb^2-2abc\\\\=(a+b)(ab+c^2)+c(a+b)^2\\\\(a+b)[ab+c^2+ca+cb]=(a+b)(b+c)(c+a)\\

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(b^3+c^3)(b-c)+(c^3+a^3)(c-a)+(a^3+b^3)(a-b)\\\\=(b^4-cb^3+c^3b-c^4)+(c^4-ac^3+a^3c-a^4)+(a^4-ba^3+ab^3-b^4)\\\\=c^3b-cb^3+a^3c-c^3a+ab^3-ba^3\\\\=c^3(b-a)+c(a^3-b^3)+ab(b^2-a^2)\\\\=(b-a)[c^3-c(b^2+a^2+ab)+ab(b+a)]\\

1 5 1
Put a=1 b=0 and verify
OK they are right but it still can be factorised
why dont u write instead of giving advises.
That's because it takes time to type such a vast answer and besides the questioners just copy the whole thing into their homework books instead of understanding it.
thanx n u r welcom