Factorise : ab^3 + bc^3 + ca^3 + a^2b^2c^2 - a^3b^2 - b^3c^2 - c^3a^2 - abc

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Q. Prove the following identities:

a b c (\sum a)^{3} - (\sum b c)^{3} = a b c \sum a^{3} - \sum b^{3} c^{2} = (a^{2} - b c) (b^{2} - c a) (c^{2} - a b)

Q. What is the LCM of

a^{3} b - a b^{3}, a^{3} b^{2} + a^{2} b^{3}

and

a b (a + b)

Q. Factorise :

a x^{2} + a b^{3}

Q. Which of the following pairs of salts will have the same relation between solubility product

(K_{s p})

and solubility (s)?

$∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & c_{3} \end{matrix} ∣ ∣ ∣ ∣ = 5, t h e n t h e v a l u e o f ∣ ∣ ∣ ∣ \begin{matrix} b_{2} c_{3} - b_{3} c_{2} & a_{3} c_{2} - a_{2} c_{3} & a_{2} b_{3} - a_{3} b_{2} b_{3} c_{1} - b_{1} c_{3} & a_{1} c_{3} - a_{3} c_{1} & a_{3} b_{1} - a_{1} b_{3} b_{1} c_{2} - b_{2} c_{1} & a_{2} c_{1} - a_{1} c_{2} & a_{1} b_{2} - a_{2} b_{1} \end{matrix} ∣ ∣ ∣ ∣ i s$

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