Factorize a5 b-a b5A- a ba2-b2B- a-ba-bC- a ba2-b2a-ba-bD- a-ba2-b2

The correct option is C ab(a^2+b^2)(a+b)(a b)ab(a^2 + b^2)(a+b)(a b) ...

Taking Out Common Factors

Factorize a5 ...

Question

Factorize $a^{5} b - a b^{5}$ .

a b (a^{2} + b^{2})

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(a + b) (a - b)

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(a - b) (a^{2} + b^{2})

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a b (a^{2} + b^{2}) (a + b) (a - b)

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Solution

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∣ ∣ ∣ ∣ ∣ \begin{matrix} a^{2} + b^{2} + c^{2} & b c + c a + a b & b c + c a + a b b c + c a + a b & a^{2} + b^{2} + c^{2} & b c + c a + a b b c + c a + a b & b c + c a + a b & a^{2} + b^{2} + c^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣

a b (a^{2} + b^{2} - c^{2}) + b c (a^{2} + b^{2} - c^{2}) - c a (a^{2} + b^{2} - c^{2})

= (a^{2} + b^{2} - c^{2}) (a b + b c - c a)

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