1. **Stating the problem:** Simplify the expression $$(7b^5 - 4b)(7b^5 + 4b)$$. 2. **Recognize the pattern:** This is in the form of $$(x - y)(x + y) = x^2 - y^2$$ where $$x = 7b^5$$ and $$y = 4b$$. 3. **Apply the difference of squares formula:** $$ (7b^5)^2 - (4b)^2 $$ 4. **Calculate each square:** $$ (7b^5)^2 = 7^2 imes (b^5)^2 = 49b^{10} $$ $$ (4b)^2 = 4^2 imes b^2 = 16b^2 $$ 5. **Subtract the results:** $$ 49b^{10} - 16b^2 $$ **Final answer:** $$ 49b^{10} - 16b^2 $$