Factor completely. $$ 242 z^{2}-18 $$

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UpStudy AI · Accepted Answer

1. Factor out the greatest common factor (GCF):
   $$
   242z^2 - 18 = 2(121z^2 - 9)
   $$

2. Recognize the expression $$121z^2 - 9$$ as a difference of two squares:
   $$
   121z^2 - 9 = (11z)^2 - 3^2
   $$

3. Factor the difference of squares using the formula:
   $$
   a^2 - b^2 = (a - b)(a + b)
   $$
   where $$a = 11z$$ and $$b = 3$$. Thus,
   $$
   (11z)^2 - 3^2 = (11z - 3)(11z + 3)
   $$

4. Write the final factorization:
   $$
   242z^2 - 18 = 2(11z - 3)(11z + 3)
   $$
$$ 242z^{2} - 18 = 2(11z - 3)(11z + 3) $$

Factor completely.

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