Answer
$\left(7x+\dfrac{1}{5}\right)\left(7x-\dfrac{1}{5}\right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
49x^2-\dfrac{1}{25}
,$ use the factoring of the difference of $2$ squares.
$\bf{\text{Solution Details:}}$
The expressions $
49x^2
$ and $
\dfrac{1}{25}
$ are both perfect squares and are separated by a minus sign. Hence, $
49x^2-\dfrac{1}{25}
,$ is a difference of $2$ squares. Using the factoring of the difference of $2$ squares which is given by $a^2-b^2=(a+b)(a-b),$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\\\\=
(7x)^2-(\frac{1}{5})^2
\\\\=
\left(7x+\dfrac{1}{5}\right)\left(7x-\dfrac{1}{5}\right)
.\end{array}
