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Expand each of the following (i)(x/2-y/3...

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

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(i)`[(x/2) - (y/3)]^2`
`=> [(x/2)^2 + (y/3)^2 - 2(x/2)(y/3)]`
`=> [(x^2)/4 + (y^3)/9 - (xy)/3]`
(ii)`x^2+(5-3)x+5xx(-3)`
`=x^2+2x-15`
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RD SHARMA-ALGEBRAIC IDENTITIES-All Questions
  1. Expand each of the following (i) (3x+4y)^2 (ii) (3x-4y)^2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. 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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  19. If : a^2+b^2+c^2-a b-b c-c a=0 , prove that a=b=c

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  20. Evaluate each of the following using identities: (i)(2x-1/x)^2 (ii...

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