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Without actually calculating the cubes. Find the value of each of the following:
(i) `(-12)^3+7^3+5^3`
(ii) `(28)^3+(-15)^3+(-13)^3`

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AI Generated Solution

To solve the given problems without actually calculating the cubes, we will use the algebraic identity for the sum of cubes: **Algebraic Identity:** If \( A + B + C = 0 \), then: \[ A^3 + B^3 + C^3 = 3ABC \] ...
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RD SHARMA ENGLISH-ALGEBRAIC IDENTITIES-All Questions
  1. Find the following products: (i) (0. 9 x+0. 7 y)(0. 81 x^2-0. 63 x y+...

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  2. If a+b+c=15 and a^2+b^2+c^2=83 , find the value of a^3+b^3+c^3-3abc

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  3. Without actually calculating the cubes. Find the value of each of th...

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

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

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

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  8. If x+1/x=6 , find (i)x^2+1/(x^2) (ii) x^4+1/(x^4)

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  9. If x^2+1/(x^2)=27 , find the values of each of the following: (i)x+1/...

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

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  11. Without actually calculating the cube: (-12)^3+7^3+5^3

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

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

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

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

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

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

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

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

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  20. 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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