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Resolve into factors a(b^2+c^2)+b(c^2+...

Resolve into factors
`a(b^2+c^2)+b(c^2+a^2)+c(a^2+b^2) + 2abc`

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KALYANI PUBLICATION-HARDER PRODUCT AND FACTORISATION -EXERCISE
  1. Resolve into factors x^2(y+2z)+y^2(x+2z)+4z^2(x+y)+4xyz

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  2. Resolve into factors 4x^2(y-z)+y^2(2x-z)+z^2(2x+y)-4xyz

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  3. Resolve into factors a(b^2+c^2)+b(c^2+a^2)+c(a^2+b^2) + 2abc

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  4. Resolve into factors (a-b)^3 +(b-c)^3+(c-a)^3

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  5. Resolve into factors a^2(b-c)+b^2(a-c)+c^2(a-b)-2abc

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  6. Resolve into factors a(b-c)^2+b(c-a)^2+c(a-b)^2+8abc

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  7. Resolve into factors x^2(2y+3z)+4y^2(3z+x)+9z^2(x+2y)+18xyz

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  8. Resolve into factors y^2(2x-z)+z^2(2x-y)-4x^2(y+z)+6xyz

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  9. Resolve into factors 12a^2b+4a^2c+9b^2c+18ab^2+2ac^2+3bc^2+18abc

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  10. Resolve into factors a(b-c)^2+b(c-a)^2+c(a-b)^2+8abc

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  11. Resolve into factors bc(b+c)-ca(c-a)-ab(b-a)-2abc

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  12. Resolve into factors 3xy(y+3x)+2yz(y+2z)+6xz(3x+2z)+12xyz

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  13. Resolve into factors x(y^2+4z^2)+y(x^2+4z^2)+2z(x^2+y^2)+4xyz

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  14. Resolve into factors x(y^2+z^2)-y(z^2+x^2)-z(x^2+y^2)+2xyz

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  15. Resolve into factors a^2b^2(a^2-b^2)+b^2c^2(b^2-c^2)+c^2a^2(c^2-a^2)

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  16. Resolve into factors a^2(b^4-c^4)+b^2(c^4-a^4)+c^2(a^4-b^4)

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  17. Resolve into factors (a^3+1)(b-c)+(b^3+1)(c-a)+(c^3+1)(a-b)

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  18. Resolve into factors x^6(y^2-z^2)+y^6(z^2-x^2)+z^6(x^2-y^2)

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  19. Resolve into factors (b-c)^3+(c-a)^3+(a-b)^3

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  20. Resolve into factors b^2c^2(b-c)+c^2a^2(c-a)+a^2b^2(a-b)

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