Factorise a 6- b 6A- a - b a - b a 2- b 2- a 2 b 2B- a - b a - b a 4- b 2- a 2 b 2C- - a - b a - b a 4- b 4- a 2 b 2D- a - b a - b a 4- b 4- ab

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Factorization of Expressions Reducible to Difference of Two Squares

Factorise a 6...

Question

Factorise $a^{6} - b^{6}$

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

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(a - b) (a - b) (a^{4} + b^{2} + a^{2} b^{2})

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= (a + b) (a - b) (a^{4} + b^{4} + a^{2} b^{2})

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(a + b) (a - b) (a^{4} + b^{4} + a b)

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(a + b) (a - b) + \frac{1}{2!} (a + b) (a - b) (a^{2} + b^{2}) + \frac{1}{3!} (a + b) (a - b) (a^{4} + a^{2} b^{2} + b^{4}) + . . .

On Resolving $a^{6} - b^{6}$ into factors give $(a + b) (a - b) (a^{2} - a b + b^{2}) (a^{2} + a b + b^{2})$ .

Question 92 (xviii)

Factorise the following using the identity $a^{2} - b^{2} = (a + b) (a - b) .$

$a^{4} - (a - b)^{4}$

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

a^{4} - b^{4}

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(a + b) (a - b) (a^{2} + b^{2}) (a^{4} + b^{4})

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