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If x = a+p, y = b+p, and z = c+p then sh...

If `x = a+p`, `y = b+p`, and `z = c+p` then show that
`x^3+y^3+z^3-3xyz ={a^3+b^3+c^3-3abc}{1+(3p)/(a+b+c)}`

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KALYANI PUBLICATION-HARDER PRODUCT AND FACTORISATION -EXERCISE
  1. If a = x+y, b=x-y and c = x+2y, then show that a^3+b^3+c^3-3abc =7y^...

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  2. If a = x+y, b = y+z, and c = z+x then show that a^3+b^3+c^3-3abc =2(...

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  3. If x = a+p, y = b+p, and z = c+p then show that x^3+y^3+z^3-3xyz ={a...

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  4. If 2s = a + b + c, Then prove that (s-a)^3+(s-b)^3+(s-c)^3-3(s-a)(s-...

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  5. If 2s = a + b + c, then prove that (s-a)^3+(s-b)^3+(s-c)^3+3 abc = s...

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  6. If 2s = a + b + c, then prove that (s-a)^3+(s-b)^3+(s-c)^3+3 abc = s...

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  7. If 2s = a + b + c, then prove that s^3 + (s-2a)^3 +(s-2b)^3 + (s-2c...

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  8. If 3s = 2(a + b + c), then prove that (s-b-c)^3 + (s-c-a)^3 +(s-a-b)...

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  9. If s= x+y+z, then prove that s^3+x^3+y^3+z^3-(s-x)^3-(s-y)^3-(s-z)^3...

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  10. If b+c=10, c+a =16, a+b=20, then prove that a^3+b^3+c^3=2567

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  11. If x = 32, y = -25, and z = -7, Then prove that x^3+y^3+z^3=16800

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  12. If x = 10 , y = 64, and z = 2, then prove that (x+y+z)^3= 438976

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

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

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

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

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  19. 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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  20. 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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