Question

factor.
$4a^2 - 49$
\\(\circ\\) a. \\((2a + 7)(2a - 7)\\)
\\(\circ\\) b. \\((2a - 7)^2\\)
\\(\circ\\) c. \\(4a(a - 49)\\)
\\(\circ\\) d. \\(4(a - 7)(a + 7)\\)

Explanation:

Step1: Identify the formula

The expression \(4a^2 - 49\) is a difference of squares. The formula for factoring a difference of squares is \(x^2 - y^2=(x + y)(x - y)\).

Step2: Rewrite the terms

Rewrite \(4a^2\) as \((2a)^2\) and \(49\) as \(7^2\). So, \(4a^2 - 49=(2a)^2 - 7^2\).

Step3: Apply the formula

Using the difference of squares formula with \(x = 2a\) and \(y = 7\), we get \((2a + 7)(2a - 7)\).

Answer:

A. \((2a + 7)(2a - 7)\)