João Flávio, o segredo do exercício é você perceber que o primeiro e o terceiro termo da equação são quadrados perfeitos, então a equação se aproxima de um trinômio quadrado perfeito, no caso:
(a² + 1)² = a4 + 2a² + 1, a única diferença é que o trinômio quadrado perfeito tem um a² a mais, então é só colocar na equação -a²:
(a² + 1)² – a² , aí teremos diferença de quadrados. a² – b² = (a+b)(a-b)
(a² + 1)² – a² = (a² + 1 + a)(a² + 1 – a)
 
espero ter ajudado.

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