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

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

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KALYANI PUBLICATION-HARDER PRODUCT AND FACTORISATION -EXERCISE
  1. 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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  2. Prove that (x-y)^3+(y-z)^3+(z-x)^3=3(x-y)(y-z)(z-x)

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

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

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

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

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

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

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  9. Prove that 4x^2(y-z)+y^2(2x-z)+z^2(2x+y)-4xyz = (2x+y)(y-z)(2x-z)

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  10. Prove that (x-a)^2/((a-b)(a-c))+(x-b)^2/((b-a)(b-c))+(x-c)^2/((c-a)(...

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  11. Prove that 1/(a(a-b)(a-c))+1/(b(b-c)(b-a))+1/(c(c-a)(c-b))=1/(abc)

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  12. Prove that a/(bc(a-b)(a-c))+b/(ca(b-c)(b-a))+c/(ab(c-a)(c-a))=1/(abc...

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  13. Prove that 2(s-a)(s-b)(s-c)+a(s-b)(s-c)+b(s-c)(s-a)+c(s-a)(s-b)=abc ...

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  14. Factorise a^3-b^3+1+3ab

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  15. If a + b + c = 0, then prove that 1/(2a^2+bc)+1/(2b^2+ca)+1/(2c^2+a...

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  16. If a^2 + b^2 + c^2 -ab-bc-ca = 0, then prove that a=b=c

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  17. If a + b + c = 0, then prove that (a+b)^2/(ab) + (b+c)^2/(bc) + (c+...

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  18. If a + b + c = 0, then prove that (2a^2)/(a^2-b^2-c^2)+(2b^2)/(b^2-...

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  19. If a + b + c = 0, then prove that (a^2+b^2+c^2)/(a^3+b^3+c^3)+2/3(1...

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  20. If a+b=c then prove that 1/(b^2+c^2-a^2)+1/(c^2+a^2-b^2)+1/(a^2+b^2...

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