Question

what is the factorization of $121b^4 - 49$?
$\bigcirc\\ (11b - 7)(11b - 7)$
$\bigcirc\\ (11b + 7)(11b - 7)$
$\bigcirc\\ (11b^2 - 7)(11b^2 - 7)$
$\bigcirc\\ (11b^2 + 7)(11b^2 - 7)$

Explanation:

Step1: Identify the form

The expression \(121b^4 - 49\) is a difference of squares. The formula for difference of squares is \(a^2 - b^2=(a + b)(a - b)\).
Here, \(a^2 = 121b^4\), so \(a=\sqrt{121b^4}=11b^2\). And \(b^2 = 49\), so \(b = 7\).

Step2: Apply the formula

Using the difference of squares formula \(a^2 - b^2=(a + b)(a - b)\) with \(a = 11b^2\) and \(b = 7\), we get \((11b^2 + 7)(11b^2 - 7)\).

Answer:

D. \((11b^{2}+7)(11b^{2}-7)\)