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Find the product: (2x-y+3z)(4x^2+y^2+9z...

Find the product: `(2x-y+3z)(4x^2+y^2+9z^2+2x y+3y z-6x z)`

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`(2x-y+3z)(4x^2+y^2+9z^2+2x y+3y z-6x z)`
It is based on this formula
`=a^3+b^3+c^3-3abc`
`=2x^3+(-y)^3+3z^3-3(2x)(-y)(3z)`
`=2x^3+(-y)^3+3z^3+18xyz`
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RD SHARMA-ALGEBRAIC IDENTITIES-All Questions
  1. If x=-2\ a n d\ y=1, by using an identity find the value: (5y + 15/y)...

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  2. Find the product: (x+y+2z)(x^2+y^2+4z^2-x y-2yz-2zx)

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  3. Find the product: (2x-y+3z)(4x^2+y^2+9z^2+2x y+3y z-6x z)

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  4. If a+b+c=6\ a n d\ a b+b c+c a=11 , find the value of a^3 + b^3 + c^3 ...

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  5. Evaluate: 30^3+20^3-50^3

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  6. If a+b+c=15\ a n d\ a^2+b^2+c^2=83 , find the value of a^3+b^3+c^3-3a ...

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  7. Evaluate: 1. 5^3-0. 9^3-0. 6^3

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  8. Without actually calculating the cub: (-12)^3+7^3+5^3

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  9. Without actually calculating the cub: (28)^3+\ (-15)^3+\ (-13)^3

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  10. If x+y+z=1,\ x y+y z+z x=-1\ \ a n d\ x y z=-1, find the value of x^3+...

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  11. Simplify: ((a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3)/((a-b)^3+(b-c)^3+(c-a...

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  12. Find the product: (3x+2y+2z)\ \ (9x^2+4y^2+\ 4\ z^2-\ 6\ x y-4\ y z-6z...

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  13. Find the product: (4x-3y+2z)\ (16 x^2+9y^2+4z^2+12 x y+6y z-8z x)

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  14. Find the product: (2a-3b-2c)(4\ a^2+\ 9\ b^2+\ 4\ c^2+\ 6\ a b-6\ b c+...

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  15. Find the product: (3x-4y+5z)\ (9x^2+16 y^2+25 z^2+12 x y-15 z x+20 y z...

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  16. If x+y+z=8\ \ a n d\ \ \ x y+y z+z x=20 , find the value of x^3+y^3+z^...

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  17. If a+b+c=9\ \ \ a n d\ \ \ a b+b c+c a=26 , find the value of a^3+b^3+...

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  18. If a+b+c=9 and a^2+b^2+c^2=35 , find the value of a^3+b^3+c^3-3a b c

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  19. Evaluate: 25^3-75^3+50^3

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  20. Evaluate: 48^3-30^3-18^3

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