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Simplify each of the following expressio...

Simplify each of the following expressions: (i) `(x+y+z)^2+(x+y/2+z/3)^2-(x/2+y/3+z/4)^2` (ii) `(x+y-2z)^2-x^2-y^2-3z^2+4x y` `-(x^2+x+1)^2-(x^2+x+1)^2`

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"(i)`=x^2+y^2+z^2+2xy+2yz+2zx+x^2+(y^2)/4+(z^2)/9+xy+yz/3+2xz/3-(x^2)/4-(y^2)/9-(z^2)/16-xy/3-yz/6-xz/4`
`=(7x^2)/4+(41y^2)/36+(151z^2)/144+(8xy)/3+(7yz)/3+(29xz)/12`
(ii) `=x^2+y^2+4z^2+2xy-4yz-2xz-x^2-y^2-3z^2+4xy-2(x^4+x^2+1+2x^3+2x+2x^2)`
`=6x^2+z^2+4x^3+4x+6xy-4yz-2xz-2x^4+2`"
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RD SHARMA-ALGEBRAIC IDENTITIES-All Questions
  1. If a+b=10 and a^2+b^2=58 , find the value of a^3+b^3

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  2. If x+1/x=7, find the value of x^3+1/(x^3)

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  3. Simplify each of the following expressions: (i) (x+y+z)^2+(x+y/2+z/3)...

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  4. Simplify each of the following: (4x+2y)^2+(4x-2y)^2 (4x+2y)^3-(4x-...

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

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

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

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

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  10. Find the products: (i)(2x+3y)\ (2x-3y)

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

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  12. Find the products: (i) (2x+y)(2x-y)(4x^2+y^2)

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

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

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  15. Evaluate each of the following by using identities: (i)0. 54 xx 0. 5...

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

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  17. If x+(1)/(x)=6, find : x^2+ (1)/(x^2)

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

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

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

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