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

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

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Resolve into factors : a^3-18abc + 27b^3+8c^3

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KALYANI PUBLICATION-HARDER PRODUCT AND FACTORISATION -EXERCISE
  1. 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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  2. 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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  3. Resolve into factors (a^3+1)(b-c)+(b^3+1)(c-a)+(c^3+1)(a-b)

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

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

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  7. Resolve into factors a^6(b^4-c^4)+b^6(c^4-a^4)+c^6(a^4-b^4)

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

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  9. Resolve into factors xy(z^2+1)+z(x^2 + y^2 )

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  10. Resolve into factors 2b^2c^2y^2z^2+2c^2a^2z^2x^2+2a^2b^2x^2y^2-a^4x^...

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  11. Resolve into factors 72y^2z^2+18z^2x^2+8x^2y^2-x^4-16y^4-81z^4

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  12. Prove that x^3+8y^3-27z^3+18xyz = (x+2y-3z)(x^2+4y^2+9z^2+3xz+6yz-2x...

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  13. Prove that a^6+8a^3+27-18a^3=(a^2+2a+3)(a^4+4a^2+9-2a^3-6a-3a^2)

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

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

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

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  17. if x+y+z=0,then Prove that (xyz)/((x+y)(y+z)(z+x))=-1 where(x!=-y,y!...

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  18. Prove that If a=2, b=3, c=5. Then prove that 2b^2c^2+2c^2a^2+2a^2b...

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  19. Prove that If 3x+2y=-1, then prove that 81x^4+16y^4+1-72x^2y^2-18x...

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  20. If x-y=7and xy=9, then find the value of (x^2+y^2)

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