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Prove that: 2a^2+2b^2+2c^2-2a b-2b c-2c...

Prove that: `2a^2+2b^2+2c^2-2a b-2b c-2c a=[(a-b)^2+(b-c)^2+(c-a)^2]`

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RD SHARMA ENGLISH-ALGEBRAIC IDENTITIES-All Questions
  1. Simplify : (4x+2y)^3+\ (4x-2y)^3

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  2. If x+y=12 and x y=27 , find the value of x^3+y^3

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  3. Prove that: 2a^2+2b^2+2c^2-2a b-2b c-2c a=[(a-b)^2+(b-c)^2+(c-a)^2]

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  4. Expand each of the following (i) (3x+4y)^2 (ii) (3x-4y)^2

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  5. Expand each of the following (i)(sqrt(2)x-3y)^2 (ii) (2x-1/(3x))^2

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  6. Expand each of the following (i)(x/2-y/3)^2 (ii) (x+5)(x-3)

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  7. Find the products: (i)(2x+3y)\ (2x-3y) (ii) (x-1)(x+1)(x^2+1)(x^4+1...

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  8. Find the products: (x-1/x)\ (x+1/x)(x^2+1/(x^2))\ (x^4+1/(x^4))

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  9. Find the products: (i) (2x+y)(2x-y)(4x^2+y^2) (ii) (x-y/5-1)\ (x+y/...

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  10. Evaluate each of the following by using identities: (i)103\ xx\ 97 ...

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  11. Evaluate each of the following by using identities: (i)(0. 99)^2 ...

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  12. Evaluate each of the following by using identities: (i)0. 54\ xx\ 0....

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  13. Evaluate each of the following by using identities: (i)95\ xx\ 96 ...

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  14. If x+1/x=6, find : x^2+\ 1//x^2

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  15. If x+1/x=6, find : x^4+1/(x^4)

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  16. If x^2+1/(x^2)=27 , find the value of each of the following: x+1/x

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  17. If x^2+1/(x^2)=27 , find the value of each of the following: x-1/x

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  18. If x+y=12 and x y=32 , find the value of x^2+y^2

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  19. If 3x+2y=12 and x y=6 , find the value of 9x^2+4y^2

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  20. If 4x^2+y^2=40\ and x y=6 , find the value of 2x+y

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