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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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If `a+b+c=0`, then `a^3+b^3+c^3=3abc`.
`=>(a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3=3(a^2-b^2)(b^2-c^2)(c^2-a^2)`
`=>(a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3=3(a-b)(a+b)(b-c)(b+c)(c-a)(c+a)`
`and (a-b)^3+(b-c)^3+(c-a)^3)=3(a-b)(b-c)(c-a)`
`=>((a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3)/((a-b)^3+(b-c)^3+(c-a)^3)=(3(a-b)(a+b)(b-c)(b+c)(c-a)(c+a))/(3(a-b)(b-c)(c-a))`
`=>((a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3)/((a-b)^3+(b-c)^3+(c-a)^3)=(a+b)(b+c)(c+a)`
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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)

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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?

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)

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

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RD SHARMA-FACTORIZATION OF ALGEBRAIC EXPRESSIONS-All Questions
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  2. Factorize : (x-2y)^3+(2y-3z)^3+(3z-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 value of x^3-8y^3-36 x y-216 , when x=2y+6.

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

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

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

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

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

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

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  12. 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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  13. 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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  14. Examples based on the middle term concepts : (i) 4sqrt3 x^2 + 5x - 2sq...

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

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

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

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  19. 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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  20. Factorize : 2sqrt(2)a^3+8b^3-27 c^3+18sqrt(2)a b c

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