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

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

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The correct Answer is:
(a+b (b+c) (c+b)
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The value of [(a^2-b^2)^3+(b^2-c^2)^3 + (c^2-a^2)^3] div [(a-b)^3+(b-c)^3+(c-a)^3 ] is equal to: (Given a ne b ne c ) [(a^2-b^2)^3+(b^2-c^2)^3 + (c^2-a^2)^3] div [(a-b)^3+(b-c)^3+(c-a)^3 ] का मान बराबर है: ( a ne b ne c दिया)

If a statement is true for all the values of the variable, such statements are called as identities. Some basic identities are : (1) (a+b)^(2)=a^(2)+2ab+b^(2)=(a-b)^(2)+4ab (3) a^(2)-b^(2)=(a+b)(a-b) (4) (a+b)^(3)=a^(3)+b^(3)+3ab(a+b) (6) a^(3)+b^(3)=(a+b)^(3)=3ab(a+b)=(a+b) (a^(2)-ab) (8) (a+b+c)^(2)=a^(2)+b^(2)+c^(2)+2ab+2bc+2ca=a^(2)+b^(2)+c^(2)+2abc((1)/(a)+(1)/(b)+(1)/(c)) (10) a^(3)+b^(3)+c^(3)-3abc=(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ca) =1/2(a+b+c)[(a-b)^(2)+(b-c)^(2)+(c-a)^(2)] If a+b+c=0,thena^(3)+b^(3)+c^(3)=3abc If a,b, c are real and distinct numbers, then the value of ((a-b)^(3)+(b-c)^(3)+(c-a)^(3))/((a-b).(b-c).(c-a))is

If a^(2)+ b^(2) + c^(2)=0 , then what is ((a^(4)-b^(4))^(3)+(b^(4)-c^(4))^(3)+(c^(4)-a^(4))^(3))/((a^(2)-b^(2))^(3)+(b^(2)-c^(2))^(3)+(c^(2)-a^(2))^(3)) equal to?

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

Simplify (a+b)(2a-3b+c)-(2a-3b)c

What will be factors of (a^(2)-b^(2))^(3) + (b^(2) -c^(2))^(3) + (c^(2) - a^(2))^(3)

Prove: |a^3 2a b^3 2b c^3 2c|=2(a-b)(b-c)(c-a)(a+b+c)

The expression (a-b)^(3)+(b-c)^(3)+(c-a)^(3) can be factorized as (a)(a-b)(b-c)(c-a)(b)3(a-b)(b-c)(c-a)(c)-3(a-b)(b-c)(c-a)(d)(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ca)

CBSE COMPLEMENTARY MATERIAL-POLYNOMIALS-Part C
  1. Simplify (x+y+z)^(3)-(x-y-z)^(2).

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  2. Factories 125x^(3)+8y^(3)+z^(3)-30xyz.

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  3. x+2 is a factor of polynomial ax^(3)+bx^(2)+x-2 and the remainder 4 is...

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  4. If the polynomials a x^3+4 x^2 + 3x -4 and x^3 - 4x + a leave the sam...

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  5. If ((9)/(10))^(3) -(2/5)^(3)-(1/2)^(3)=(x)/(50), find x

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  6. If (x-3) and (x-1/3) are factors of the polynomial px^(2)+3x+r, show t...

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  7. Using identify, find the value of (-7)^(3)+(5)^(3)+(2)^(3).

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  8. Find the dimensions of cube whose volume is given by the expression. 4...

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  9. Given possible expression for the length and breadth of each of the fo...

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  10. A literacy caompaign was organised by Class IX girl students under NSS...

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  11. Under tree plantation programme students of Class IX planted total (3x...

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  12. I f a+b+c=0,f i n d t h e v a l u e((b+c)^2)/(b c)+((c+a)^2)/(c a)+((a...

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  13. 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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  14. .Factorise: (2a-b-c)^(3)+(2b-c-a)^(3)+(2c-a-b)^(3)

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  15. If the polynomial 4x^(3)-16x^(2)+ax+7 is exactly divisible by x-1, the...

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  16. If p,q & r are all non zero and p+q+r=0, prove that p^(2)/(qr)+(q^(2))...

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  17. Factories 9x^(3)-27x^(2)-100x+300

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  18. If (x+4) is a factor of the polynomial x^(3)-x^(2)-14x+24, find the ot...

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  19. x/y+y/x=-1( w h e r e ,x , y!=0) then find the value of x^3-y^3

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  20. (155xx155+155xx55+55xx55)/(155xx155xx155-55xx55xx55)

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