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Factorisation Using Algebraic Identities

xviii Factori...

Question

Question 92 (xviii)

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

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

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Solution

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

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Factorisation Using Algebraic Identities

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