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The factors of x^3-1+y^3+3x y are (a) (x...

The factors of `x^3-1+y^3+3x y` are (a) `(x-1+y)(x^2+1+y^2+x+y-x y)` (b)`(x+y+1)(x^2+y^2+1-x y-x-y)` (c)`(x-1+y)(x^2-1-y^2+x+y+x y)` (d)`3(x+y-1)(x^2+y^2-1)`

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Correct option is (A)
`x^3-1+y^3+3x y=(x)^2+(-1)^2+y^3-3xx(x)xx(-1)xxy`
We know,
`a^3+b^3+c^3-3abc=(a+b+c)\(a^2+b^2+c^2-ab+bc-ca)`
`x^3-1+y^3+3x y=[x+(-1)+y]\[x^2+-1^2-x\(-1)-(-1)\y-yx]`
`=(x-1+y)(x^2+1+y^2+x+y-xy)`
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RD SHARMA-FACTORIZATION OF ALGEBRAIC EXPRESSIONS-All Questions
  1. If a^2+b^2+c^2=250 and a b+b c+c a=3, find a+b+c

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  2. Write the value of 25^3-75^3+50^3,If a+b+c=0

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  3. Write the value of 48^3-30^3-18^3

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  4. Write the value of (1/2)^3+(1/3)^3-\ (5/6)^3

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  5. Write the value of 30^3+20^3-50^3

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  6. The factors of a^2-1-2x-x^2 are (a)(a-x+1)(a-x-1) (b)(a+x-1)(a-x+1) (c...

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  7. The factors of x^4+x^2+25 are (a)(x^2+3x+5)(x^2-3x+5) (b)(x^2+3x+5)(x...

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  8. The factors of x^2+4y^2+4y-4x y-2x-8 are (a)(x-2y-4)(x-2y+2) (b) (x-y...

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  9. The factors of x^3-x^2y-x y^2+y^3 are (a(x+y)(x^2-x y+y^2) (b) (x+y...

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  10. The factors of x^3-1+y^3+3x y are (a) (x-1+y)(x^2+1+y^2+x+y-x y) (b)...

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  11. The factors of 8a^3+b^3-6a b+1 are (a) (2a+b-1)(4a^2+b^2+1-3a b-2a) ...

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  12. (x+y)^3−(x−y)^3 can be factorized as  (a) 2y(3x^2+y^2) (b) 2x(3x^2+y...

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  13. The factors of x^3-7x+6 are

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  14. The expression (a-b)^3+\ (b-c)^3+\ (c-a)^3 can be factorized as (a)(a-...

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  15. The expression x^4+4 can be factorized as (a) (x^2+2x+2)(x^2-2x+2) (...

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  16. If 3x=a+b+c , then the value of (x-a)^3+\ (x-b)^3+\ (x-c)^3-3\ (x-a)(x...

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  17. If (x+y)^3-\ (x-y)^3-6y\ (x^2-y^2)=\ k y^3, then k= (a)1 (b) 2 (c) ...

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  18. If x^3-3x^2+3x+7=(x+1)(a x^2+b x+c),\ then a+b+c= (a)4 (b) 12 (c) ...

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  19. The value of ((2. 3)^3-\ 0. 027\ )/((2. 3)^2+\ 0. 69+0. 09) is (a)2 (b...

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  20. The value of ((0. 013)^3+\ (0. 007)^3)/((0. 013)^2-\ 0. 013\ xx\ 0. 00...

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