One of the factors of $(25 x^{2} - 1) + (1 + 5 x)^{2}$ is
(a) 5+x (b) 5-x (c) 5x-1 (d) 10x

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Solution

ANSWER:
$(25 x^{2} - 1) + (1 + 5 x)^{2}$
$= (5 x - 1) (5 x + 1) + (1 + 5 x)^{2} = (5 x + 1) ((5 x - 1) + (1 + 5 x)) = (5 x + 1) 10 x$
So, the factors of are (5 x + 1) and 10 x
Hence, the correct answer is option (d).

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