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

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

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If a ,b ,c are in A.P., prove that: i. (a-c)^2=4(a-b)(b-c) ii. a^2+c^2+4a c=2(a b+b c+c a) iii. a^3+c^3+6a b c=8b^3

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RD SHARMA ENGLISH-ALGEBRAIC IDENTITIES-All Questions
  1. Find the product: (3x+2y+2z)\ \ (9x^2+4y^2+\ 4\ z^2-\ 6\ x y-4\ y z-6z...

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

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  3. 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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  4. 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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  5. 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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  6. 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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  7. 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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  8. Evaluate: 25^3-75^3+50^3

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

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  10. Evaluate: (1/2)^3+\ (1/3)^3-\ \ (5/6)^3

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  11. Evaluate: (0. 2)^3-\ (0. 3)^3+\ (0. 1)^3

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  12. If x+1/x=3, then find the value of x^2+1/(x^2)

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  13. If x+1/x=3, then the value of x^6+1/x^6is.

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  14. If a+b=7\ \ a n d\ \ a b=12 , find the value of a^2+b^2

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  15. If a-b=5 and a b=12 , find the value of a^2+b^2

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  16. If x-1/x=1/2 , then write the value of 4x^2+4/(x^2)

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  17. If a^2+1/(a^2)=102 , find the value of a-1/a

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  18. If a+b+c=0 , then write the value of (a^2)/(b c)+(b^2)/(c a)+(c^2)/(a ...

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  19. If x+1/x=5, then x^2+1/(x^2)=? (a)25 (b) 10 (c) 23 (d) 27

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  20. If x+1/x=2, then x^3+1/(x^3)=? (a)64 (b) 14 (c) 8 (d) 2

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