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Factor the expression.

[tex]\( 49x^2 - 16 \)[/tex]

A. [tex]\( (4x + 7)(4x - 7) \)[/tex]

B. [tex]\( (4x - 7)(4x - 7) \)[/tex]

C. [tex]\( (7x - 4)(7x - 4) \)[/tex]

D. [tex]\( (7x + 4)(7x - 4) \)[/tex]

Sagot :

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]