Question:
One of the factors of $\left(25 x^{2}-1\right)+(1+5 x)^{2}$ is
(a) $5+x$
(b) $5-x$
(c) $5 x-1$
(d) $10 x$
Solution:
$\left(25 x^{2}-1\right)+(1+5 x)^{2}$
$=(5 x-1)(5 x+1)+(1+5 x)^{2}$
$=(5 x+1)[(5 x-1)+(1+5 x)]$
$=(5 x+1)(10 x)$
So, the factors of $\left(25 x^{2}-1\right)+(1+5 x)^{2}$ are $(5 x+1)$ and $10 x$
Hence, the correct answer is option (d).
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