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If x=3\ a n d\ y=-1, find the values of ...

If `x=3\ a n d\ y=-1,` find the values of each of the using identity: `(9y^2-4x^2)(81 y^4+36 x^2y^2+16 x^4)`

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we know that,
`a^3-b^3=(a-b)(a^2+ab+b^2)`
using this formula,
we can write it as,
`(9y^2-4x^2)(81 y^4+36 x^2y^2+16 x^4)`
`=(9y^2)^3-(4x^2)^3`
now putting the values of x and y from question
`=[9(-1)^2]^3-[4(3)^2]^3`
`=(9)^3-(36)^3`
`=729-46656`
`=-45927`
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RD SHARMA-ALGEBRAIC IDENTITIES-All Questions
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  2. Find the products: (x^3+1)(x^6-x^3+1)

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  3. If x=3\ a n d\ y=-1, find the values of each of the using identity: (9...

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  4. If x=3\ a n d\ y=-1, find the values of each of the using identity: (3...

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  5. If x=3\ a n d\ y=-1, find the values of each of the using identity: (x...

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  6. If x=3\ a n d\ y=-1, find the values of each of the using identity: (x...

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  7. If x=3\ a n d\ y=-1, find the values of each of the using identity: (5...

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  8. If a+b=10\ \ a n d\ \ \ a b=16 , find the value of a^2-a b+b^2\ a n d\...

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  9. If a+b=8\ \ a n d\ \ a b=6, find the value of a^3+b^3

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  10. If a-b=6\ \ a n d\ \ a b=20 , find the value of a^3-b^3

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  11. If x=-2\ a n d\ y=1, by using an identity find the value: (4y^2-9x^2)(...

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  12. If x=-2\ a n d\ y=1, by using an identity find the value: (2/x - x/2...

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  13. If x=-2\ a n d\ y=1, by using an identity find the value: (5y + 15/y)...

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  14. Find the product: (x+y+2z)(x^2+y^2+4z^2-x y-2yz-2zx)

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  15. Find the product: (2x-y+3z)(4x^2+y^2+9z^2+2x y+3y z-6x z)

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  16. If a+b+c=6\ a n d\ a b+b c+c a=11 , find the value of a^3 + b^3 + c^3 ...

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  17. Evaluate: 30^3+20^3-50^3

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  18. If a+b+c=15\ a n d\ a^2+b^2+c^2=83 , find the value of a^3+b^3+c^3-3a ...

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  19. Evaluate: 1. 5^3-0. 9^3-0. 6^3

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  20. Without actually calculating the cub: (-12)^3+7^3+5^3

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