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Find the division of (a^3+b^3-c^3+3abc...

Find the division of
`(a^3+b^3-c^3+3abc) -: (a+b-c)`

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In the formula, a^3+b^3+c^3-3 abc = 1/2 (a+b+c){(a-b)^2+(b-c)^2+(c-a)^2} , if a + b + c != 0 , Show that if a^3 +b^3+c^3= 3abc impliesa=b=c

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KALYANI PUBLICATION-HARDER PRODUCT AND FACTORISATION -EXERCISE
  1. Resolve into factors : (3x-y)^2-2(3x-y)-35

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  2. Find the division of (x^3+y^3-3xy+1)-:(x+y+1)

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  3. Find the division of (a^3+b^3-c^3+3abc) -: (a+b-c)

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  4. Find the division of (8a^3-27b^3-72ab-64)-:(2a-3b-4)

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  5. Find the division of (x^3+8y^3-27z^3+18xyz)-:(x+2y-3z)

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  6. Find the division of (a^3+b^3+27-9ab)-:{(a-b)^2+(b-3)^2+(3-a)^2}

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  7. Find the division of (27x^3-64y^3-8-72xy)-:{(3x+4y)^2+(3x+2)^2+(4y-2...

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  8. Find the division of {a^3+8-9b(3b^2-2a)}-:(a^2+9b^2+4-2a+3ab+6b)

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  9. Find the product of the following. (x^2+y^2+z^2+xy+xz-yz) (x-y-z)

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  10. Find the product of the following. (a^2+b^2+c^2-ab+bc+ca) (a+b-c)

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  11. Find the product of the following. (x^2+9y^2+4-3xy-2x-6y) (x+3y+2)

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  12. Find the product of the following. (p^2+4q^2+r^2+2pq+pr-2qr) (p-2q-r...

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  13. Find the product of the following. (4x^2+9y^2+z^2+6xy+2xz-3yz) (2x-3...

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  14. Find the product of the following. (a^2+4b^2+2ab-3a+6b+9)(a-2b+3)

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  15. Find the product of the following. (9a^2+25b^2+15ab+12a-20b+16)(3a-5...

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  16. Find the product of the following. (9x^2+16y^2+12xy+6x-8y+4)(3x-4y-...

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  17. If x-2y = 4 then prove that x^3-8y^3-24xy-64=0

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  18. If x-y=6 then prove that x^3-y^3-18xy-216=0

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  19. If a + 2b = 4c, then prove that a^3+8b^3-64c^3+24abc=0

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  20. If x = b + c - 2a, y = c + a-2b , z = a + b-2c, then prove that x^3...

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