Question

homework: 6.7b (obj 2) factor a difference of squares
question 2, 6.7.15
hw score: 33.33%, 5 of 15 points
points: 0 of 1
factor.
256c² - 196
select the correct choice below and, if necessary, fill in the answer box within your choice.
a. 256c² - 196 =
b. the polynomial is prime.

Explanation:

Step1: Identify perfect - squares

We know that \(256c^{2}=(16c)^{2}\) and \(196 = 14^{2}\).

Step2: Apply difference - of - squares formula

The difference - of - squares formula is \(a^{2}-b^{2}=(a + b)(a - b)\). Here \(a = 16c\) and \(b = 14\), so \(256c^{2}-196=(16c + 14)(16c-14)\). We can further factor out a 2 from each factor: \((16c + 14)(16c-14)=2(8c + 7)\times2(8c-7)=4(8c + 7)(8c-7)\).

Answer:

A. \(4(8c + 7)(8c-7)\)