We can see that we are subtracting to squares, [tex]49x^2[/tex] and 16. Since we are subtracting two squares, we can simplify the expression using the difference of squares formula, which is:
[tex]a^2 - b^2 = (a + b)(a - b)[/tex]
We know [tex]a^2 = 49x^2[/tex] and [tex]b^2 = 16[/tex], so we will need to find [tex]a[/tex] and [tex]b[/tex]. Each one can be found as such:
[tex]a^2 = 49x^2[/tex]
[tex][tex]\sqrt{a^2} = \sqrt{49x^2}[/tex]
[tex]a = \sqrt{49} \cdot \sqrt{x^2}[/tex]
[tex]a = 7x[/tex]
[tex]b^2 = 16[/tex]
[tex]\sqrt{b^2} = \sqrt{16}[/tex]
[tex]b = 4[/tex]
Thus, we can say the following:
[tex]49x^2 - 16 = \boxed{(7x + 4)(7x - 4)}[/tex]
Our answer is (7x + 4)(7x - 4).
