# One of the factors of

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).