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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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To simplify the expression \[ \frac{(a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3}{(a-b)^3+(b-c)^3+(c-a)^3} \] we can follow these steps: ...
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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)

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

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

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?

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)

RD SHARMA-ALGEBRAIC IDENTITIES-All Questions
  1. Without actually calculating the cub: (28)^3+\ (-15)^3+\ (-13)^3

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  2. If x+y+z=1,\ x y+y z+z x=-1\ \ a n d\ x y z=-1, find the value of x^3+...

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

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  5. Find the product: (4x-3y+2z)\ (16 x^2+9y^2+4z^2+12 x y+6y z-8z x)

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  6. Find the product: (2a-3b-2c)(4\ a^2+\ 9\ b^2+\ 4\ c^2+\ 6\ a b-6\ b c+...

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  7. Find the product: (3x-4y+5z)\ (9x^2+16 y^2+25 z^2+12 x y-15 z x+20 y z...

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  8. If x+y+z=8\ \ a n d\ \ \ x y+y z+z x=20 , find the value of x^3+y^3+z^...

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  9. If a+b+c=9\ \ \ a n d\ \ \ a b+b c+c a=26 , find the value of a^3+b^3+...

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  10. If a+b+c=9 and a^2+b^2+c^2=35 , find the value of a^3+b^3+c^3-3a b c

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  11. Evaluate: 25^3-75^3+50^3

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  12. Evaluate: 48^3-30^3-18^3

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  13. Evaluate: (1/2)^3+\ (1/3)^3-\ \ (5/6)^3

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  14. Evaluate: (0. 2)^3-\ (0. 3)^3+\ (0. 1)^3

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  15. If x+1/x=3, then find the value of x^2+1/x^2

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  16. If x+1/x=3, then the value of x^6+1/x^6is.

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  17. If a+b=7\ \ a n d\ \ a b=12 , find the value of a^2+b^2

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  18. If a-b=5 and a b=12 , find the value of a^2+b^2

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  19. If x-1/x=1/2 , then write the value of 4x^2+4/(x^2)

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  20. If a^2+1/(a^2)=102 , find the value of a-1/a

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