Answer
Error: $(9x)^{2}\neq 9x^{2}.$
The correct term is $3x, $ because $(3x)^{2}=9x^{2}.$
Correct factorization: $(3x+7)(3x-7)$
Work Step by Step
The square of 7 is 49, but the square of $9x$ is $81x^{2}$, not $9x^{2}.\\\\$
In applying the formula $a^{2}-b^{2}=(a+b)(a-b)$,
here, $a=3x$, and $b=7$
So, the correct way to factor is
$9x^{2}-49=(3x+7)(3x-7)$
