Question

Factorise (a^2 - 5a)^2 - 36

Answer 1

$(a^2 - 5a)^2 - 36 \\ \\ (a^2 - 5a)^2 - 6^2 \\ \\ (a^2-5a+6)(a^2-5a-6) \\ \\ (a^2-2a-3a+6)(a^2+a-6a-6)\\ \\ (a(a-2)-3(a-2))(a(a+1)-6(a+1)) \\ \\ (a-3)(a-2)(a-6)(a+1) \\ \\ \bold{(a+1)(a-2)(a-3)(a-6)}$

$\therefore\ (a^2 - 5a)^2 - 36=\bold{(a+1)(a-2)(a-3)(a-6)}$

Answer 2

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