1. The problem is to express $8c^2 - 2b^2$ as a difference of two squares. 2. Recall the difference of squares formula: $$a^2 - b^2 = (a - b)(a + b)$$ 3. First, factor out the common factor from both terms: $$8c^2 - 2b^2 = 2(4c^2 - b^2)$$ 4. Now focus on the expression inside the parentheses: $4c^2 - b^2$. 5. Recognize that $4c^2 = (2c)^2$ and $b^2 = b^2$, so this is a difference of squares. 6. Apply the difference of squares formula: $$4c^2 - b^2 = (2c - b)(2c + b)$$ 7. Substitute back: $$8c^2 - 2b^2 = 2(2c - b)(2c + b)$$ Final answer: $$8c^2 - 2b^2 = 2(2c - b)(2c + b)$$