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

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

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RD SHARMA ENGLISH-FACTORIZATION OF ALGEBRAIC EXPRESSIONS-All Questions
  1. 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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  2. Factorize : 2sqrt(2)a^3+8b^3-27 c^3+18sqrt(2)a b c

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

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

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

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

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  7. Factorize each of the following expressions : x(x+z)-y(y+z)

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  8. Factorize each of the following expressions : a^2-b^2-a-b

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  9. Factorize each of the following expressions : 25 x^2-10 x+1-36 y^2

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  10. Factorize each of the following expressions : 1-2a b-(a^2+b^2)

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  11. Factorize each of the following expressions: a b(a^2+b^2-c^2)+b c...

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  12. Factorize each of the following expressions: x(x^2+y^2-z^2)+y(-...

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  13. Factorize each of the following expressions by splitting the middle ...

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  14. Factorize each of the following expressions by splitting the middle ...

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

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  16. Factorize of the expression: a^3x+a^2(x-y)-a(y+z)-z\

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

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

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  19. Factorize each of the following expressions: (i)(5x-1/x)^2+4\ (5x-1...

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  20. Factorise: (i) 4x^2+9y^2+16 z^2+12 x y-24 y z-16 x z (ii) 2x^2+y^...

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