Sure, let's factor the given expression:
[tex]\[ 49x^2 - 16 \][/tex]
Notice that this is a difference of squares. The difference of squares formula is:
[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]
First, we identify [tex]\(a\)[/tex] and [tex]\(b\)[/tex] such that [tex]\(a^2 = 49x^2\)[/tex] and [tex]\(b^2 = 16\)[/tex].
1. For [tex]\(49x^2\)[/tex]:
[tex]\[
a = 7x \quad \text{since} \quad (7x)^2 = 49x^2
\][/tex]
2. For [tex]\(16\)[/tex]:
[tex]\[
b = 4 \quad \text{since} \quad 4^2 = 16
\][/tex]
Now, applying the difference of squares formula:
[tex]\[ 49x^2 - 16 = (7x)^2 - 4^2 = (7x - 4)(7x + 4) \][/tex]
Therefore, the factored form of the expression [tex]\(49x^2 - 16\)[/tex] is:
[tex]\[ (7x - 4)(7x + 4) \][/tex]
Thus, the correct answer is:
D. [tex]\((7x + 4)(7x - 4)\)[/tex]
