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Prove that : (a+b)^3+(b+c)^3+(c+a)^3-3(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)`

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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)

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

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

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Prove that : |{:(a,b,c),(b,c,a),(c,a,b):}|=3 a b c-a^(3)-b^(3)-c^(3)

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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)

RD SHARMA ENGLISH-FACTORIZATION OF ALGEBRAIC EXPRESSIONS-All Questions
  1. Factorize each of the following expressions : x^4+x^2+1 (ii) x^4+5x^2...

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

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  3. 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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  4. Factorize each of the following expressions: (i)4a^2+12 a b+9b^2-8a-...

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

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

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  7. Factorize each of the following algebraic expressions : x^8-y^8 (i...

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  8. 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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  9. Factorize : 64 a^3+125 b^3+240 a^2b+300 a b^2

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  10. Factorize each of the following expressions : (i) 4sqrt(3)x^2+5x-2sqr...

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

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  12. Factorize : p^3(q-r)^3+q^3(r-p)^3+r^3(p-q)^3

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

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

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

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  17. Resolve a^3-b^3+1+3a b into factors.

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

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  19. Factorize each of the following expressions : x^2+2x y+y^2-a^2+2a...

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  20. Factorize each of the following expressions : 3-12(a-b)^2

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