The expression $100a^2 - 49$ is a difference of squares, which can be simplified using the identity $x^2 - y^2 = (x+y)(x-y)$. In this case:

$100a^2 - 49 = (10a)^2 - 7^2$

Applying the difference of squares formula:

$(10a)^2 - 7^2 = (10a + 7)(10a - 7)$

Therefore, the simplified form of $100a^2 - 49$ is $(10a + 7)(10a - 7)$.