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If 2x+3y=13 and x y=6, find the value of...

If `2x+3y=13` and `x y=6,` find the value of `8x^3+27 y^3`

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RD SHARMA ENGLISH-ALGEBRAIC IDENTITIES-All Questions
  1. Expand each of the following: (i)(3x+4y)^2 (ii) (3x-4y)^2

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

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  3. If 2x+3y=13 and x y=6, find the value of 8x^3+27 y^3

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  4. If a+b=10 and a^2+b^2=58 , find the value of a^3+b^3

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

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

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  7. Simplify : (4x+2y)^3+\ (4x-2y)^3

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

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

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

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

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

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

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

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

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

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

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

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

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