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

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

A

`3(x+2y)(2y-3z) (3z-x)`

B

`3(x-2y)(2y+3z) (3z-x)`

C

`3(x-2y)(2y-3z) (3z+x)`

D

`3(x-2y)(2y-3z) (3z-x)`

Text Solution

Verified by Experts

The correct Answer is:
D
we known that
`a^(3)+b^(3)+c^(3)-3abc=(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ca)`
Also if a+b+c=0 then `a^(3) +b^(3)+c^(3)=3abc`
here, we see that `(x-2y)+(2y-3z)+(3z-x)=0`
therefore , `(x-2y)^(3)+(2y-3z)^(3)+(3z-x)^(3)=3(x-2y)(2y-3z) (3z-x)`
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NCERT EXEMPLAR-POLYNOMIALS-Polynomials
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  4. find the following products (i) ((x)/(2)+2y)((x^(2))/(4)-xy+4y^(2...

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  5. Factorise (i) 1+64x^(3)" "(ii) a^(3)-2sqrt(2)b^(3)

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

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

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  14. if both x-2 and x-(1)/(2) are factors of px^(2)+5x+r. then show ...

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  15. Without actual division, prove that 2x^4-5x^3+2x^2-x+2 is exactly divi...

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  16. Simplify :(2x-5y)^3-(2x+5y)^3

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  17. Multiply: x^2+4y^2+z^2+2x y+x z-2y z\ by x-2y-z

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  18. if a, and c are all non zero and a+b+c=0 , then find the value of...

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  19. If a+b+c=5 and ab+bc+ca=10, then find a^3+b^3+c^3-3abc

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  20. Prove that (a+b+c)^3 - a^3-b^3-c^3 = 3(a+b)(b+c)(c+a).

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