1. The problem asks to find which expression is equivalent to $50x^2 - 128$. 2. We start by factoring the expression $50x^2 - 128$. 3. First, factor out the greatest common factor (GCF) from both terms: $$50x^2 - 128 = 2(25x^2 - 64)$$ 4. Notice that $25x^2 - 64$ is a difference of squares, which can be factored using the formula $$a^2 - b^2 = (a - b)(a + b)$$ where $a = 5x$ and $b = 8$. 5. Applying the difference of squares formula: $$25x^2 - 64 = (5x - 8)(5x + 8)$$ 6. Substitute back into the expression: $$2(25x^2 - 64) = 2(5x - 8)(5x + 8)$$ 7. Therefore, the expression equivalent to $50x^2 - 128$ is $2(5x - 8)(5x + 8)$. 8. Comparing with the options, this matches option C. Final answer: C 2(5x - 8)(5x + 8)