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Factorize : (x-2y)^3+(2y-3z)^3+(3z-x)^3...

Factorize : `(x-2y)^3+(2y-3z)^3+(3z-x)^3`

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To factorize the expression \((x - 2y)^3 + (2y - 3z)^3 + (3z - x)^3\), we can use the identity for the sum of cubes. The identity states that: \[ a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - ac - bc) \] In our case, we can set: - \(a = (x - 2y)\) ...
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RD SHARMA-FACTORIZATION OF ALGEBRAIC EXPRESSIONS-All Questions
  1. Factorize the following expression : (2x-3y)^3+(...

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  2. Factorize : (a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3

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  3. Factorize : (x-2y)^3+(2y-3z)^3+(3z-x)^3

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  4. Simplify: ((a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3)/((a-b)^3+(b-c)^3+(c-a)...

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  5. Find the value of x^3-8y^3-36 x y-216 , when x=2y+6.

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  6. Factorize the following expression : x^4+x^2+1

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  7. Factorize each of the following expressions: 2p(a-b)+3q(5a-5b)+4r(2a...

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  8. Prove that : (a+b)^3+(b+c)^3+(c+a)^3-3(a+b)(b+c)(c+a)=2(a^3+b^3+c^3-3a...

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  9. Factorize the following expression: 4a^2+12 a b+9b^2-8a-12 b

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  10. Factorisation by grouping the terms: (x^2+3x)^2-5(x^2+3x)-y(x^2+3x)+5y

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  11. Factorize each of the following expressions : 4a^2-9b^2-2a-3b

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  12. Factorize each of the following algebraic expressions : x^8 - y^8 a...

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  13. Factorize: (i) 8x^3+27 y^3+z^3-18 x y z, (ii) a^3-8b^3-64 c^3-24 a...

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  14. Factorize : 64 a^3+125 b^3+240 a^2b+300 a b^2 8/(27)x^3+1+4/3x^2+2x...

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  15. Examples based on the middle term concepts : (i) 4sqrt3 x^2 + 5x - 2sq...

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  16. Factorize : (x^2-4x)(x^2-4x-1)-20

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  17. Factorize : p^3(q-r)^3+q^3(r-p)^3+r^3(p-q)^3

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  18. Factorize : (x-y)^3+(y-z)^3+(z-x)^3

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  19. Factorize : 2sqrt(2)x^3+3sqrt(3)y^3+sqrt(5)(5-3sqrt(6)x y)

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  20. Prove that : a^3+b^3+c^3-3a b c=1/2(a+b+c){(a-b)^2+(b-c)^2+(c-a)^2}

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