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

Factorize : `p^3(q-r)^3+q^3(r-p)^3+r^3(p-q)^3`

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To factorize the expression \( p^3(q-r)^3 + q^3(r-p)^3 + r^3(p-q)^3 \), we can follow these steps: ### Step 1: Identify the structure of the expression We notice that the expression consists of three terms, each of which is a cube. This suggests that we might be able to use the identity for the sum of cubes. ### Step 2: Define variables for simplification Let: - \( A = p(q - r) \) ...
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If p = -2, q = - 1 and r = 3, find the value of (i) p^(2) + q^(2) - r^(2) (ii) 2p^(2) - q^(2) + 3r^(2) (iii) p - q - r (iv) p^(3) + q^(3) + r^(3) + 3 pqr (v) 3p^(2) q + 5pq^(2) + 2 pqr (vi) p^(4) + q^(4) - r^(4)

If the equation px^(3)+3qx^(2)y+3rxy^(2)+sy^(3)=0 (p,q,r,s!=0) represents three coincident lines,then (A) (p)/(q)=(q)/(r)=(r)/(s) (B) pr=qs (C) q=s (D) p=r

If a,b,c denote the sides of triangleABC , show that the value of the expression, a^3 (p-q)(p-r)+b^2(q-r)+b^2(q-r)(q-p)+c^2(r-p)(r-q) cannot be negative where p,q,r in R .

RD SHARMA-FACTORIZATION OF ALGEBRAIC EXPRESSIONS-All Questions
  1. Examples based on the middle term concepts : (i) 4sqrt3 x^2 + 5x - 2sq...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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