Factorise the following $64 a^{2} + 1$

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Solution

$64 a^{2} + 1 = (8 a)^{2} + 1^{2} = (8 a + 1)^{2} - 16 a = (8 a + 1)^{2} - (4 \sqrt{a})^{2} 64 a^{2} + 1 = (8 a - 4 \sqrt{a} + 1) (8 a + 4 \sqrt{a} + 1)$

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