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Prove that (a-2b)^3+(2b-c)^3+(c-a)^3 =...

Prove that
`(a-2b)^3+(2b-c)^3+(c-a)^3 =3(a-2b)(2b-c)(c-a)`

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KALYANI PUBLICATION-HARDER PRODUCT AND FACTORISATION -EXERCISE
  1. Prove (a+2b)^3+(b+2c)^3+(c+2a)^3+3(a+3b+2c)(b+3c+2a)(c+3a+2b)=27(a+b+...

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  2. Prove that (3x-2y)^3+(y-2z)^3+(y+2z-3x)^3=3(3x-2y)(y-2z)(y+2z-3x)

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  3. Prove that (a-2b)^3+(2b-c)^3+(c-a)^3 =3(a-2b)(2b-c)(c-a)

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  4. Prove that (a+c)^3-(b+c)^3-(a-b)^3=3(a+c)(b+c)(a-b)

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  5. Prove that (x+2y+3z)^3-x^3-8y^3-27z^3=3(2y+3z)(x+3z)(x+2y)

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  6. prove 8(a+b+c)^3-(a+b)^3-(b+c)^3-(c+a)^3=3(a+b+2c)(a+2b+c)(2a+b+c)

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  7. Prove that 8a^3-(a+b)^3-(a-c)^3-(c-b)^3=3(a-b)(a+c)(2a+b-c)

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  8. Prove that a^3-(2a-b-c)^3+(b-2c)^3-(2b-c-a)^3=3(b+c-a)(a+b-2c)(2a-2b...

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  9. Prove that 64(x+y+z)^3-(2x+y+z)^3-(x+2y+z)^3-(x+y+2z)^3=3(3x+3y+2z)(...

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  10. Prove that (b+c-a)^3+(c+a-b)^3+(a+b-c)^3-(a+b+c)^3+108abc = 84abc

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  11. Prove that (b+c)^3+(c+a)^3+(a+b)^3-3(b+c)(c+a)(a+b) =2(a^3+b^3+c^3-3...

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  12. Prove that (a-b)^3+(b-c)^3+(c-a)^3=3(a-b)(b-c)(c-a)

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  13. Prove that (3x-2y)^3+(y+2z)^3+(y-2z-3x)^3=3(3x-2y)(y+2z)(y-2z-3x)

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  14. Prove that (a-2b)^3+(2b-1)^3+(1-a)^3=3(a-2b)(2b-1)(1-a)

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  15. Factorise (5x+3y+z)(15xy+3yz+5xz)-15xyz

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  16. Factorise (2a+b+c)(2ab+bc+2ca)-2abc

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  17. Factorise (2a+3b+4c)(6ab+8ac+12bc)-24abc

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  18. Factorise (a-b+2c)(2ca-2bc-ab)+2abc

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  19. Factorise (a-2b-3c)(6bc-2ab-3ac)-6abc

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  20. Resolve into factors 9a^2(2b+c)+4b^2(3a+c)+c^2(3a+2b)+12abc

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