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Factorise : 8x^3+y^3+27 z^3-18 x y z....

Factorise : `8x^3+y^3+27 z^3-18 x y z`.

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To factorize the expression \(8x^3 + y^3 + 27z^3 - 18xyz\), we can use the identity for the sum of cubes and the product of three variables. The identity states: \[ a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - ac - bc) \] ### Step 1: Identify \(a\), \(b\), and \(c\) ...
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NCERT ENGLISH-POLYNOMIALS-SOLVED EXAMPLES
  1. Find the remainder when x^4+x^3-2x^2+x+1 is divided by x-1.

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  2. Write the following cubes in the expanded form:(i)(3a + 4b)^3\ \ \ \ ...

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  3. Factorise : 8x^3+y^3+27 z^3-18 x y z.

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  4. Factorise 8x^3+27 y^3+36 x^2y+54 x y^2.

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  5. Check whether -2\ a n d\ 2 are zeroes of the polynomial x+2.

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  6. Find the value of each of the following polynomials at the indicated ...

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  7. Find the degree of each of the polynomials given below:(i) x^5-x^4+3 ...

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  8. Divide the polynomial 3x^4-4x^3-3x-1by x-1

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  9. Divide p(x)by g(x), where p(x) = p(x)=x+3x^2-1and g(x)=1+x

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  10. Verify whether 2 and 0 are zeroes of the polynomial x^2-2x.

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  11. Find a zero of the polynomial p(x)=2x+1.

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  12. Factorise: (i) 49 a^2+70 a b+25 b^2 (ii) (25)/4x^2-(y^2)/9

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  13. Write (3a\ +\ 4b\ +\ 5c)^2in expanded form.

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  14. Check whether the polynomial q(t)=4t^3+4t^2-t-1is a multiple of 2t+1

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  15. Examine whether x+2 is a factor of x^3+3x^2+5x+6 and of 2x+4.

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  16. Find the value of k, if x-1is a factor of 4x^3+3x^2-4x+k.

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  17. Factorise 6x^2+17 x+5 by splitting the middle term, and by using the ...

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  18. Factorise y^2-5y+6 by using the Factor Theorem.

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  19. Factorise x^2-23 x^2+142 x-120 .

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  20. Find the following products using appropriate identities:(i)\ (x+3)\ ...

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