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The expression (a-b)^3+\ (b-c)^3+\ (c-a)...

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-a b-b c-c a)`

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(a-b)^3 + (b-c)^3 + (c-a)^3=? (a) (a+b+c)(a^2+b^2+c^2-ab-bc-ac) (b) 3(a-b)(b-c)(c-a) (c) (a-b)(b-c)(c-a) (d)none of these

The value of [{(a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3}/{(a-b)^3+(b-c)^3+(c-a)^3}] = (1) 3(a+b)(b+c)(c+a) (2) 3(a-b)(b-c)(c-a) (3) (a+b)(b+c)(c+a) (4) 1

Factorise : (a+b)^3+(b+c)^3+(c+a)^3-3(a+b)(b+c)(c+a)

Factorise : (a+b)^3+(b+c)^3+(c+a)^3-3(a+b)(b+c)(c+a)

If (a-b),\ (b-c),(c-a) are in G.P. then prove that (a+b+c)^2=3(a b+b c+c a)

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

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

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

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

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 b c)

RD SHARMA ENGLISH-FACTORIZATION OF ALGEBRAIC EXPRESSIONS-All Questions
  1. If a^2+b^2+c^2=250 and a b+b c+c a=3, find a+b+c

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  2. Write the value of 25^3-75^3+50^3

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  3. Write the value of 48^3-30^3-18^3

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  4. Write the value of (1/2)^3+(1/3)^3-\ (5/6)^3

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  5. Write the value of 30^3+20^3-50^3

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  6. The factors of a^2-1-2x-x^2 are (a)(a-x+1)(a-x-1) (b)(a+x-1)(a-x+1)...

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  7. The factors of x^4-x^2-10x-25 are (a)(x^2+3x+5)(x^2-3x+5) (b)(x^2+3x+...

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  8. The factors of x^2+4y^2+4y-4x y-2x-8 are (a)(x-2y-4)(x-2y+2) (b) (x...

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  9. The factors of x^3-x^2y-x y^2+y^3 are (a(x+y)(x^2-x y+y^2) (b) (x...

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  10. The factors of x^3-1+y^3+3x y are (a) (x-1+y)(x^2+1+y^2+x+y-x y) (...

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  11. The factors of 8a^3+b^3-6a b+1 are (a) (2a+b-1)(4a^2+b^2+1-3a b-2a) ...

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  12. (x+y)^3−(x−y)^3 can be factorized as   (a) 2y(3x^2+y^2) (b) 2x(3x^2...

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  13. The factors of x^2-7x+6 are

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  14. The expression (a-b)^3+\ (b-c)^3+\ (c-a)^3 can be factorized as (a)(a...

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  15. The expression x^4+4 can be factorized as (a) (x^2+2x+2)(x^2-2x+2) ...

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  16. If 3x=a+b+c , then the value of (x-a)^3+\ (x-b)^3+\ (x-c)^3-3\ (x-a)(x...

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  17. If (x+y)^3-\ (x-y)^3-6y\ (x^2-y^2)=\ k y^3, then k= (a)1 (b) 2 (...

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  18. If x^3-3x^2+3x+7=(x+1)(a x^2+b x+c),\ then a+b+c=

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  19. The value of ((2. 3)^3-\ 0. 027\ )/((2. 3)^2+\ 0. 69+0. 09) is (a)2 ...

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  20. The value of ((0. 013)^3+\ (0. 007)^3)/((0. 013)^2-\ 0. 013\ xx\ 0. 00...

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